1.) Car 2 will overtake car 1 at t = 0.828 seconds after car 1 took off. 2.) Point of overtaking will happen at a distance of 2.69 m from the starting point. 3.) Car 2 will be 3.71 m/s faster than Car 1 at the point of overtaking.
What is Acceleration?In mechanics, acceleration is the measure of how quickly the velocity of an object changes in relation to time.
1.) As, distance = initial velocity * time + (1/2) * acceleration * time^2
Given, car 1 has an acceleration of 3.5 m/s^2 and car 2 has an acceleration of 6.1 m/s^2.
So, distance = (6.1 m/s^2) * (t + 1.1)^2 = (3.5 m/s^2) * t^2
Therefore, car 2 will overtake car 1 at t = 0.828 seconds after car 1 took off.
2.)As, distance = initial velocity * time + (1/2) * acceleration * time^2
Let t be the time it takes for car 2 to overtake car 1, as calculated above t=0.828 seconds.
distance covered by car 1
distance = (1/2) * 3.5 m/s^2 * t^2 = (1/2) * 3.5 m/s^2 * 0.828^2 = 0.907 m
And distance covered by Car 2 is:
distance = (1/2) * 6.1 m/s^2 * (t+1.1)^2 = (1/2) * 6.1 m/s^2 * (0.828+1.1)^2 = 2.69 m
Therefore, point of overtaking will happen at a distance of 2.69 m from the starting point.
3.) As we know, velocity = acceleration * time
point of overtaking is at t = 0.828 seconds after car 1 took off.
So, Velocity of Car 1 at the point of overtaking is:
velocity = 3.5 m/s^2 * 0.828 sec = 2.94 m/s
Velocity of Car 2 at the point of overtaking is:
So, velocity = 6.1 m/s^2 * (0.828 + 1.1) sec = 6.65 m/s
Therefore, Car 2 will be 6.65 m/s - 2.94 m/s = 3.71 m/s faster than Car 1 at the point of overtaking.
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Note: The question given on the portal is incomplete. here is the complete question.
Question: Two rather unequal cars are competing in a drag race. for simplicity, let's assume that the accelerations of the cars are constant. car 1 has an acceleration of 3.5 m/s2, while car 2 has an acceleration of 6.1 m/s2. car 2 gets off to a late start, 1.1 seconds after car 1.
1. At what time after Car 1 took off will it be overtaken by Car 2?
2. How far down the track will this happen?
3. How much faster will Car 2 be than Car 1 by that time?
the change in velocity between location d and location f: select an option unanswered the change in momentum between location d and location f: select an option unanswered the average net force between location
The change in the momentum is equal to the product of the mass and the change in the velocity.
what is change in momentum?
The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. This applied force can increase or decrease the momentum or even change the object's direction.The change in momentum = m × (v – u). Here a = [(v - u)t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality. The SI units of mass and acceleration are kg and m s-2 respectively.Δ p = F net Δ t . F net Δ t F net Δ t is known as impulse and this equation is known as the impulse-momentum theorem. From the equation, we see that the impulse equals the average net external force multiplied by the time this force acts. It is equal to the change in momentum.To learn more about momentum refers to:
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a reactor operates at a power of 103 mw(t) for 1 year. calculate the power from decay heat a. 1 day following shutdown, b. 1 month following shutdown, c. 1 year following shutdown.
So the heat dacy can be calculated using the winger way formula
In one day ,[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t), In one month =[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t) , in one year , [tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)
According to thermodynamics, heat is a type of energy that crosses a thermodynamic systems' boundary due to a temperature differential across the barrier Heat is absent in thermodynamic systems. However, the expression is also regularly used to describe the thermal energy that constitutes a system's internal energy and is reflected in the system's temperature. In all senses of the word, energy is a form of heat.
For the decay we have winger way formula as ,
[tex]P_{d} =0.0622P_{0}[t-0.2-(t_{0}-0.2(t_{0}+t)-0.2][/tex]
[tex]P_{0}=1.5GW(t)[/tex],[tex]t_{0}=31,536,000[/tex]
[tex]P_{d}(t)=\\[/tex]thermal power generation due to beta and gamma rays
[tex]t_{0}=[/tex]time in seconds , of thermal power level before shut down
t= rime , in seconds elapsed since the shutdown
a) In one day ,
Number of seconds ,t=86400s
so , P
[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [86,400-0.2-(31,536,000+86,400)-0.2]
[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t)
b ) In one month
Number of seconds ,t=2629800s
[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [2629800-0.2-(31,536,000+2629800)-0.2]
[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t)
c) In one year
Number of seconds ,t=2629800s
[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [31,536,000-0.2-(15,768,000+31,536,000)-0.2]
[tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)
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work and Tes...
As shown in the drawing, a positively charged particle B has
charge q = +6.1 x 104 C. The particle lies between particles C
and A whose charges, respectively, are qA= - 10 x 10 -4 ℃ and qc
+17.3 x 104 C. The distance between A and B is 0.73 m and
the distance between C and B is 1.09 m. What is the magnitude
of the net force on particle B due to the other two particles?
Please round your answer to the nearest whole number (integer).
Take k as 9.0 x 10⁹ Nm²/C².
=
A
B
Equation: In general,
F = k12. Use this equation twice,
7-2
one for A and B, another for C and B.
The magnitude of the n.et force on particle B due to the other two particles is 8 x 10¹⁹ N
What is the net force on particle B due to the other two particles?The net force on particle B due to the other two particles is calculated by applying the formula for electric force.
F = ( kq₁q₂) / r²
where;
K is Coulomb's constantq₁ is first chargeq₂ is second charger is the distance between the chargesElectric force between A and B;
F(AB) = ( 9 x 10⁹ x 10 x 10⁻⁴ x 6.1 x 10⁴ ) / ( 0.73² )
F (AB) = 1.03 x 10¹² N
Electric force between B and C;
F(BC) = ( 9 x 10⁹ x 17.3 x 10⁴ x 6.1 x 10⁴ ) / ( 1.09² )
F (BC) = 8 x 10¹⁹ N
The net force on particle B is calculated as;
F (net) = - F (AB) - F (BC)
F (net) = - 1.03 x 10¹² N - 8 x 10¹⁹ N
F (net) = - 8 x 10¹⁹ N
F (net) = 8 x 10¹⁹ N towards A
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Which of the following solutions contains the smallest total concentration of ions, assuming complete dissociation?
a) 2 M AI2(SO4)3
b) 2 M AICl3
c) 2 M NaCl
d) 2 M CaCl2
The solution with the lowest total ion concentration, assuming full dissociation, is 2 M aluminum sulphate.
What is concentration?Concentration in chemistry is defined as the abundance of an ingredient divided by the total volume of a combination. There are four sorts of mathematical descriptions: mass concentration, molar concentration, number concentration, and volume concentration. The amount of a material, such as salt, that is present in a certain amount of tissue or liquid, such as blood. When there is less water present, a material becomes more concentrated. When a person does not drink enough water, the salt in his or her urine may become more concentrated. A substance's concentration is the amount of solute contained in a given amount of solution. Molarity is the number of moles of solute in one liter of solution and is used to express concentrations.
Here,
The solution with the lowest total ion concentration, assuming full dissociation, is 2 M aluminum sulfate.
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pls answer it
thanks
(a) The change in the length of the bar is 0.012 m.
(b) The new length of the bar is 10.012 m.
What is the change in length of the bar?The change in the length of the bar is calculated by applying the following formula.
ΔL = αLΔθ
where;
α is the linear expansivityL is the original length of the barΔθ is the change in lengthΔL = ( 24 x 10⁻⁶ x 10) x ( 40 - -10)
ΔL = ( 24 x 10⁻⁶ x 10) x ( 50)
ΔL = 0.012 m
The new length of the bar is calculated as follows;
L₁ = L + ΔL
L₁ = 10 m + 0.012 m
L₁ = 10.012 m
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a softball is thrown off of a building that is 80 meters high at a velocity of 10 meters per second. its height, in meters, after t seconds is
When a softball is thrown from an 80-meter-high building at a velocity of 10 meters per second, the height after t seconds is 148 feet.
What is velocity?Velocity is a vector representation of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also known as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s). The direction of movement of the body or item is defined by velocity. Speed is fundamentally a scalar number. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change. Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number.
Here,
The maximum height the ball will reach is the vertex of the parabola s(t)=48+80t-16t2. first, we need to solve for t. The vertex of any parabola of the form f(x)=ax2+bx+c is found by using x=-b/2a. In this case, x=t, b=80 and a=-16. Substituting we get:
]t=-80/((2)(-16)--->t=-80/-32--->t=5/2
Putting this value of t in the original formula will give us the maximum height:
s(t)=48+80t-16t2
s(5/2)=48+80(5/2)-16(5/2)2
s(5/2)=48+200-16(25/4)
s(5/2)=248-100
smax=148 feet
It's height, in meters, after t seconds is 148 feet when softball is thrown off of a building that is 80 meters high at a velocity of 10 meters per second.
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Model rocket engines are rated by their thrust force and by the impulse they provide. You can use this information to determine the time interval at which the engines fire. Two rockel engines provide the same impulse. The first engine provides 6 N of thrust for 2 s; the second provides 4 N of thrust. For how long does this second engine fire? A. 1 s B. 2 s C. 3 s D. 4 s
The answer is B. 2 s. The impulse provided by both engines is the same, so they must fire for the same amount of time in order to provide that amount of impulse.
What is engines?Engines are devices that convert energy into mechanical force, usually to power machines and vehicles. Engines come in a variety of forms and sizes, but all are based on the same basic principles of converting thermal energy into mechanical force via combustion.
Since the first engine fires for 2 s and provides 6 N of thrust,
the second engine must also fire for 2 s to provide 4 N of thrust (since 6N/2s = 4N/x, where x = 2s).
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1. Two balls with masses of 2.0kg and 60kg traveling at 12ms and 4.0 m/s, respectively. They have a
head-on inelastic collision (not perfectly). The 2.0kg moves in the opposite direction with a speed of 8.0
m/s.
a. Find the speed of the 6.0kg ball after the collision.
B. Find the KE for each ball before and after the collision
C. Find the amount of KE that is lost during the collision.
a) The speed of the 60 Kg ball is 4.1 m/s
b) The KE before and after collision is 144 J and 64 J respectively
c) The KE lost is 80 J
What is the momentum?We know that when we talk about the momentum, our minds would go to the collision of the objects that we have in this case which are the balls in the question.
a) Momentum before collision = Momentum after Collison
(2 * 12) + (4 * 60) = (8 * 2) + (60 * v)
v is the velocity of the 60Kg ball
24 + 240 = 16 + 60v
v = 4.1 m/s
b) KE before collision
1) 0.5 * 2 * (12)^2 = 144 J
2) 0.5 * 60 * 4^2 = 480 J
KE after collision;
1) 0.5 * 2 * 8^2 = 64 J
2) 0.5 * 60 * (4.1)^2 = 504.3 J
c) The KE lost in the collision is; 144 J - 64 J = 80 J
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Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 3.1cm . Two of the particles have a negative charge: q1 = -8.4nC and q2 = -16.8nC . The remaining particle has a positive charge, q3 = 8.0nC . What is the net electric force acting on particle 3 due to particle 1 and particle 2?
1. Find the net force ?F? 3 acting on particle 3 due to the presence of the other two particles. Report you answer as a magnitude ?F3 and a direction ? measured from the positive x axis. Express the magnitude in newtons and the direction in degrees to three significant figures
2. Assume that particle 3 is no longer fixed to a corner of the triangle and is now allowed to move. In whatdirection would particle 3 move the instant after being released? Draw the velocity vector for particle 3 below. The orientation of your vector will be graded, but not its length
1. The net force is 79.1°
The angle between those two forces is 120 degrees (because the triangle is equilateral) so the net force on particle 3 is the vector sum of the two forces.
The direction of the force on particle 3 due to particle 1 is along the line joining particles 1 and 3. The direction of the force on particle 3 due to particle 2 is along the line joining particles 2 and 3.
To find the net electric force acting on particle 3 due to particles 1 and 2, we can use Coulomb's law, which states that the force between two point charges is given by the equation:
[tex]F = k * (q1 * q2) / r^2[/tex]
where F is the force, k is the Coulomb constant [tex](8.99 x 10^9 N * m^2/C^2)[/tex], q1 and q2 are the charges of the two particles, and r is the distance between the two particles.
In this case, we have three particles placed at the corners of an equilateral triangle, with a side length of 3.1 cm. Since the triangle is equilateral, all three sides are equal in length, so r1 = r2 = 3.1 cm
The net force on particle 3 is the vector sum of the two forces acting on it due to particles 1 and 2.
F3 = F31 + F32 where F31 is the force on particle 3 due to particle 1 and F32 is the force on particle 3 due to particle 2
[tex]F31 = k * (q3 * q1) / r1^2[/tex]
[tex]F32 = k * (q3 * q2) / r2^2[/tex]
[tex]F31 = 8.99 x 10^9 N * m^2/C^2 * (8.0 nC * -8.4 nC) / (3.1 cm)^2[/tex]
[tex]F32 = 8.99 x 10^9 N * m^2/C^2 * (8.0 nC * -16.8 nC) / (3.1 cm)^2[/tex]
[tex]F31 = -9.52 * 10^{-4 N}[/tex]
[tex]F32 = -1.93 * 10^{-3 N}[/tex]
[tex]F3 = F31 + F32 = -2.88 * 10^{-3 N}[/tex]
After solving, The net force = 79.1°
The direction of the force on particle 3 due to particle 1 is along the line joining particles 1 and 3. The direction of the force on particle 3 due to particle 2 is along the line joining particles 2 and 3.
The angle between those two forces is 120 degrees (because the triangle is equilateral) so the net force on particle 3 is the vector sum of the two forces
2. Particle 3 will move in the direction of the net force acting on it, which is the vector sum of the two forces acting on it due to particles 1 and 2.
Since the net force is [tex]-2.88 * 10^{-3 N}[/tex], and the angle between the direction of the forces on particle 3 due to particles 1 and 2 is 120 degrees, particle 3 will move in the direction of the angle bisector of the angle between those two forces.
The angle bisector of 120 degrees is 60 degrees, thus the net force is acting on particle 3 at 60 degrees with respect to the positive x-axis.
The instant after being released, particle 3 will move in the direction of the net force vector and it will have a velocity vector pointing in the same direction as the net force.
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Please answer the question.
The angle θ between P and Q vector is 18.43°.
What is vector quantity?In physics, a vector is a quantity that has both magnitude and direction. It is typically represented by an arrow with the same direction as the quantity and a length proportional to the magnitude of the quantity.
A vector, while having magnitude and direction, does not have position. A vector quantity is any physical quantity that has both directions and magnitude.
According to given parameters:
PQ sinθ = (1/3) PQ cosθ
tanθ = 1/3
θ = 18.43°
Hence, the angle θ between P and Q vector is 18.43°
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How far does the object travel between 5 and 10 s
The distance travelled by the object between 5 and 10 seconds is 25 m.
What is the distance travelled by the object?The area under velocity time graph gives the distance travelled by the object.
The distance travelled by the object between 5 and 10 seconds is calculated from the area of curve within this time range.
Area of the curve between 5 and 10 seconds = Area of triangle
Distance travelled between 5 and 10 seconds = Area of triangle formed between 5 and 10 seconds
Area of triangle = ¹/₂bh
where;
b is the base of the triangleh is the height of the triangleA = ¹/₂ x (10 - 5 ) x ( 10 )
A = 25 m
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ou have a lightweight spring whose unstretched length is 4.0 cmcm. first, you attach one end of the spring to the ceiling and hang a 1.4 gg mass from it. this stretches the spring to a length of 5.1 cmcm . you then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. this stretches the spring to a length of 4.6 cmcm . Required:
What is the magnitude of the charge (in nC) on each bead?
The magnitude of the charge on each bead is 7.08nc.
What is the magnitude of charge?Given the following information:
Original length = 4.0 cm converted to m = 0.04 m
1.4 grams to kilograms = 0.0014
5.1 cm to m = 0.051 is the new length.
4.6 cm to m = 0.046 m is the final length.
e = 0.051 - 0.046
= 0.005m in length
Scientific evidence:
Gravitational acceleration = 9.8m/s²
Coulomb's constant is equal to 8.99 x 10⁹ Nm²/C²
We would use Coulomb's law to calculate the magnitude of the charge (in nC) on each bead:
First, we would calculate the spring constant of this lightweight spring
using the following formula:
W = mg = Ke
K = mg/e
K = 0.014 x 9.8 / 0.05
K = 2.744N/m
K, the spring constant, is 2.744N/m.
In terms of electrostatic force:
F = ke
F = 2.77 x 0.05
F = 0.1385
F equals 0.1385 Newton.
Coulomb's electrostatic force law.
The charge in an electric field can be calculated mathematically using the following formula:
q = √F/k x r
We get by substituting the given parameters into the formula;
q = √(0.1385/8.99 x 10⁹) x 0.046
q = √(1.54060 x 10⁻¹²) x 0.046
q = 7.08 x 10⁻⁸
Take note that 1 nC = 1 x 10⁻⁹ C
Charge, q = 7.08nc
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fill in the blank.the internal revenue service threatens chloe with a penalty if she fails to pay her back taxes. she pays, and the threat is withdrawn. in the future, she is more prompt in meeting her obligation. this is an example of the use of___to control behavior. group of answer choices
When a person or business avoids paying their tax responsibilities, it is a criminal violation that entails fines and penalties.
What do "tax avoidance" or "tax evasion" mean?If Chloe doesn't pay her overdue taxes, then Internal Revenue Service will impose penalties. The threat is removed after she makes a payment. Now, she will finish her work more swiftly. This illustrates the application of behavior control.
What is the name for legitimate tax avoidance?On the contrary hand, tax avoidance is entirely legal. Qualified taxpayers may claim a variety of deductions, credits, or income adjustments in accordance with IRS regulations. For instance, some homeowners are permitted to write off the interest they pay off their mortgage.
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What is the average speed of the car during the first hour of the trip? (2 point
O 1 miles/hour
5 miles/hour
40 miles/hour
O 25 miles/hour
Answer:40 miles/hour
which of the following is true about the line in relation to the plane ? group of answer choices the line lies on the plane. the line intersects the plane in one point. the line is parallel to the plane.
The line 1-0+t2 in relation to the plane x-2y+z =1 is parallel to the plane as both points satisfy the plane equation.
A plane is a two-dimensional, Euclidean surface which never ends in the mathematics. A plane is a point's (zero dimensions), a line's (one dimensions), and space's (three dimensions) two-dimensional equivalents.
A line is a network of interconnected points that can go on forever in both the directions. Three noncollinear points, two parallel lines, or two intersecting lines can all be used to form a plane. If two points are on the same line, they are said to be collinear.
The question is incomplete, find the complete question here
which of the following is true about the line 1-0+t2 in relation to the plane x-2y+z =1 ? group of answer choices
the line lies on the plane.
the line intersects the plane in one point.
the line is parallel to the plane.
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Help me pleaseee!!
Would appreciate ^^
**BRAINLIST, thanks and
points***
With steps pls so I can
understand
The battery has an internal resistance of 2.50
4.1 Show that the resistance of the 6.2 V, 4.5 W lamp at its working potential difference
(pd) is about 9.
Look at photo for more info
4.2 The terminal pd across the battery is 6.2 V.
Calculate the emf of the battery.
The resistance of working potential difference of the 6.2 V, 4.5 W lamp is 8.54 ohm. When terminal pd across the battery is 6.2 V, the emf of the battery is 8.01 V.
What is resistance?The opposition that a substance provides to the flow of electric current is referred to as resistance. The uppercase letter R represents it. The ohm is the standard unit of resistance, which is sometimes written as a word and sometimes represented by the uppercase Greek letter omega. Resistance is a measure of an electrical circuit's resistance to current flow. Resistance is measured in ohms, which is represented by the Greek letter omega ().
Here,
r=2.5 ohm
V= 6.2 volts
P=4.5 watt
P=V²/R
R=V²/P
R=6.2*6.2/4.5
R=8.54 ohm that is about 9 ohm.
I=V/R
I=0.726 A
EMF=V+Ir
=6.2+0.726*2.5
=6.20+1.81
=8.01 volts
The resistance of the 6.2 V, 4.5 W lamp at its working potential difference is 8.54 ohm. The emf of the battery when terminal pd across the battery is 6.2 V is 8.01 V.
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A pulley system has a mechanical advantage of 3, and an object weighing 9 Newtons must be lifted 15
meters. How much force must be applied to lift the object?
Use the following equation to find the answer.
MA= Fo/F i
(1 point)
A. 1.7 N
b. 0.3 N
c.27 N
d.3N
C. 27 N force must be applied to lift the object.
How much force must be applied to lift the object?The mechanical advantage of a pulley system is calculated by dividing the output force by the input force. In this case, the mechanical advantage is 3, meaning the output force is 3 times larger than the input force.To find the force required to lift the object, we can use the equation: Force = (Weight of Object x Distance) / Mechanical Advantage.Plugging in the given numbers, the force required to lift the object is (9 Newtons x 15 meters) / 3 = 45 Newtons. Therefore, 45 Newtons of force must be applied to lift the object. Using a pulley system to lift an object is advantageous because it reduces the amount of force needed to lift the object. The mechanical advantage of the pulley system multiplies the output force, allowing the user to lift the object with less effort.Pulley systems are often used to lift large or heavy objects, such as in cranes and construction sites.They are also useful in machines and everyday items, such as roller blinds and bicycles.
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classify each of the following substances as an element, compound, or mixture using the dropdown menus in the classification table.
Each sort of atom in an element is unique. The joining of two or more distinct atoms results in a compound. In a mixture, two or more distinct substances are combined but not chemically bonded.
Is CO2 a combination of elements or a compound?With two oxygen atoms and one carbon atom, carbon dioxide, or CO2, is a chemical molecule.Each sort of atom in an element is unique. The joining of two or more distinct atoms results in a compound. In a mixture, two or more distinct substances are combined but not chemically bonded.A crystal-like lattice of the two ions Na+ and Cl- makes up the ionic compound salt, which is composed of two ions. Many sodium chloride molecules can be found in salt water.Carbon, Hydrogen, and Oxygen, which are joined by covalent bonds, make up the organic molecule known as vitamin D. Any chemical species that consists of two or more components is called a compound.To learn more about compound refer to:
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which of the following sketches and choice of coordinate axis best describe the physical situation presented in this problem?
A negative acceleration indicates that you will reduce the velocity's present value, while a positive acceleration indicates that you will increase it.
How can one tell whether an acceleration is positive or negative?According to mathematics, a negative acceleration indicates that you will reduce the velocity's present value, while a positive acceleration indicates that you will increase it.A horizontal line can be seen on the acceleration-time graph in its negative area (negative acceleration).The slope of a line is positive (+) if it slopes uphill from left to right. The slope of a line is negative if it slopes downward from left to right (-). A positive slope in our pizza example indicates that as we add more toppings (x), the overall price of the pizza (y) also rises.To learn more about acceleration refer to:
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You’re at the ice-skating rink with a 5kg bowling ball. The two of you (you and the bowling ball) stand motionless in the middle of the rink so that your combined momentum is zero. You then throw the bowling ball and begin to slide backward. If your momentum is then 12 kg • m/s backward, what is speed does the bowling ball have?
The speed of the bowling ball is 2.4 m/s forward.
What is the speed of the bowling ball?
The speed of the bowling ball is calculated by applying the principle of conservation of linear momentum as shown below.
P1 = -P2
where;
P1 is your momentumP2 is the momentum of the bowling ballP1 = -mv
-P1 = mv
where;
m is the mass of the bowling ballv is the speed of the bowling ballThe speed of the bowling ball is calculated as;
v = ( - 12 kgm/s ) / ( 5 kg )
v = -2.4 m/s
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find the largest natural number m such that n 3 - n is divisible by m for all n e n. prove your assertion.
Since the sum of the odd term coefficients and the even term coefficients must both be zero, the expression a0+a1k+a2k2++ankn is divisible by 3 for all kN.
What is the greatest integer that can divide each natural number n by n3?Number `n3n is divisible by 6 because there is a multiple of two in a pair of consecutive numbers and a multiple of three in a triplet of consecutive integers.Since the sum of the odd term coefficients and the even term coefficients must both be zero, the expression a0+a1k+a2k2++ankn is divisible by 3 for all kN.Equation n3−n=n(n2−1)=n(n+1)(n−1). There must be at least one even number among these three consecutive integers. Furthermore, 3 must divide one of the integers using the same reasoning. As n3n is divisible by 2 and 3, it follows that it is divisible by 6, too.To learn more about consecutive numbers refer to:
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A 75-kg object traveling 25 m/s collides with and sticks to a 315-kg object initially at rest. What is the final velocity of the two objects?
19 m/s
12 m/s
4.8 m/s
2.9 m/s
The final velocity of the two objects is 4.8m/s.
What does the word "velocity" mean?
The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity. The meter per second (m/s) is the accepted unit of velocity magnitude (also known as speed). Alternately, the magnitude of velocity can be expressed in centimeters per second (cm/s).
The change in velocity between the objects following a collision is known as the relative velocity. When particles collide, momentum and energy are transferred, which results in a change in velocity. It abides under the rule of conservation of energy and momentum.
m1 = 75kg
m2 = 75+315kg = 390kg
v1 = 25m/s
v2 = ?
Initial momentum = m1*v1
Final momentum = m2*v2
Initial momentum = Final momentum
m1v1 = m2v2
75*25 = 390 *v2
v2 = 75*25/390
v2 = 4.8m/s
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A certain lightning bolt moves 22.7 C of charge. How many fundamental units of charge is this? Your answer will be in the form of: N x 1019 and you need to indicate the number N, do not include the unit.
Hint: e = 1.6 x 10-19 C.
The fundamental units of charge is 14.18 C for moving 22.7C of charge.
An object's ability to feel an attractive or repulsive force toward another is determined by its electric charge, also known as charge for short. The coulomb is the primary measure of charge (C). There are two forms of charge: protons exhibit positive charge, while electrons exhibit negative charge (exhibited by electrons). The electric forces between charged particles are described by Coulomb's law; if the charges shift, the electromagnetic force becomes more complex.
fundamental charge=[tex]\frac{q}{e}[/tex]
Now, n=[tex]\frac{22.7}{1.6\times10^{-19} }[/tex]
n=[tex]1.418\times10^{20}[/tex]
and according to question,
the value of fundamental unit charge is 14.18.
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A loaded ore car has a mass of 950 kg and rolls on rails with negligible friction. IT starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0o above the horizontal The car accelerates uniformly to a speed of 2.20 m/s in 12.0 s and then continues at constant speed. What power must the winch motor provides when the car is moving at constant speed?
10.628 kW of power must the winch motor provides when the car is moving at constant speed at the slope of 30.0o at a speed of 2.20m/s for 12 s to keep of moving.
The maximum Force, with the maximum speed of the motor, gives maximum power Now we know
a = (vf-vi)/t = (2.20 - 0)/12 => 0.1853 m/s^2
The maximum force is when the car is accelerating so,
f = fa+fg
F = ma+ ma * sign 30o => 4831.035 N ( As shown in the Image attached how the perpendicular vector that is a signθ is taken)
So the force will be 4831.035 N
Hence the maximum power p = fxV
4831.035 * 2.20
P =10626.27 w
which results in 10626.27/1000 kW
So 10.628 Kw is the maximum power required for the slop of 30o.
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consider the prpositions p anmd q where pis you can paddle one canoe down the river and q is you can paddle one kayak down the river
The propositions P and Q are both true. P states that you can paddle one canoe down the river, and Q states that you can paddle one kayak down the river. Both of these activities are possible, making both statements true.
What is propositions?A proposition is a statement or assertion that expresses a judgment or opinion about a particular topic or issue. It is a type of argument used in logic and critical thinking, and is typically expressed in a declarative sentence. Propositions can be either true or false and can be used to support or reject a claim. In philosophy, propositions can also be used to explain and justify a particular belief or set of beliefs. Propositions are often used in academic and scientific discourse to communicate ideas and arguments in a concise and logical manner.
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If you could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr) across oceans and space, approximately how long would it take to drive to the nearest star, Alpha Centauri (4.4 light-years away)?
If you could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr) across oceans and space, approximately how long would it take to drive around Earth's equator?
If one could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr), the time it will take to drive around the Earth's equator is 250.47hours.
How to calculate time?The time it will take to cover a certain distance can be calculated using the following formula;
Speed = distance ÷ time
According to this question, one could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr) across oceans and space. The distance around Earth at the Equator, its circumference, is 40,075 kilometers (24,901 miles).
Time = Distance ÷ speed
Time = 40,075km ÷ 160km/hr
Time = 250.47hours
Therefore, 250.47hours is the time it will take to cover around the Earth's equator.
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the support bearings at a and b allow free turning of the shaft. (figure 1) figure1 of 1 part a determine the resultant internal torque acting on the cross section at points c and d . enter your answers in newton-meters to three significant figures separated by a comma.
The internal torque acting at point C is 800 lb-ft clockwise, and at point D is 1500 ft-lb anti-clockwise.
The shaft is bearing at a and b. As the shaft is at rest and not rotating in any direction. So the internal torque must be balancing the external torques acting on the shaft. Near the bearing A, the the external torque acting on the shaft is 1500 lb-ft clockwise, so at point D there must be an anti-clockwise torque. So the torque acting on the D is 1500 ft-lb.
Similarly, near the bearing B the external torque acting on the shaft is 800 lb-ft anti-clockwise, so there must be an equal and external clockwise torque working on point C to balance the 800 anti-clockwise torque. So the internal torque working on point C is 800 lb-ft.
--The given question is incomplete, the complete question is:
"the support bearings at a and b allow free turning of the shaft. (figure 1) figure1 of 1 part a determine the resultant internal torque acting on the cross section at points c and d . enter your answers in newton-meters to three significant figures separated by a comma."
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A pendulum that consists of a 2kg mass swings a maximum vertical displacement of 10 cm above its rest position. At its lowest point, the KE of the mass is equal to
F. 0.196 J
G. 1.96 J
H. 19.6 J
J. 196 J
K. 1960 J
The kinetic energy at the lowest point is 1.96 Joule. The result is obtained by using the concept of Conservation of mechanical energy.
What is the conservation of mechanical energy?The Conservation of mechanical energy states that the total mechanical energy of a system is conserved. It can be expressed as
E initial = E final
KE₁ + U₁ = KE₂ + U₂
½mv₁ + mgh₁ = ½mv₂ + mgh₂
Where
E = mechanical energyKE = kinetic energyU = potential energym = mass of an objectv = speed of objecth = height of objectThe index 1 and 2 shows at point 1 (initial) and 2 (final).
A pendulum that consists of
m = 2 kgh max = 10 cm (0.1 m) above its rest position.At its lowest point, find kinetic energy!
The lowest point is at the mean position where h = 0.
Let's say, point 1 is at the highest point and point 2 is at the lowest point.
E initial = E final
½mv₁ + mgh₁ = ½mv₂ + mgh₂
At the highest, the speed is zero. h max means highest position. It would be
½m(0) + mgh₁ = ½mv₂ + mg(0)
mgh₁ = ½mv₂
U₁ = KE₂
The kinetic energy is
KE₂ = mgh₁
KE₂ = 2 (9.8) (0.1)
KE₂ = 1.96 Joule
Hence, the kinetic energy at the lowest point is 1.96 Joule.
The correct option is (G).
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Sally, Max, and William are on a camping trip in the forest. They are riding their bikes through the forest and come across a clearing. In the clearing, there are several trees and a small plane. Sally is curious about the physics of the plane, so she asks Max and William to help her measure the distance from the plane to the nearest tree. They use a measuring tape to find that the distance is 60 meters. They also measure the height of the plane to be 10 meters and the height of the tree to be 20 meters. Using the principles of physics, they calculate the angle at which the plane is flying relative to the tree. What is the angle?
Answer: The angle at which the plane is flying relative to the tree is 19.47 degrees.
Explanation:
To calculate the angle at which the plane is flying relative to the tree, we can use the principle of trigonometry and the Pythagorean theorem. Since we know the distance from the plane to the nearest tree (60 meters), the height of the plane (10 meters), and the height of the tree (20 meters), we can use these measurements to form a right triangle with the plane, the tree, and the ground.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse of the right triangle. The length of the hypotenuse is the distance between the plane and the top of the tree. The hypotenuse is calculated by the square root of (distance^2 + height of the plane^2 + height of the tree^2)
The angle we are trying to calculate is opposite to the height of the tree, therefore we can use the tangent function:
tan(angle) = opposite/adjacent
opposite = height of the tree = 20m
adjacent = distance = 60m
angle = arctan(20/60) = arctan(1/3) = 19.47122063449069 degrees
The angle at which the plane is flying relative to the tree is 19.47 degrees.
two objects are located on an airtrack. the magnitude of the charge on object a is 3 times higher than on object b, and object a also has a 6 times higher mass than object b. which one of the following is true for the magnitudes of the accelerations (not drawn to scale or necessarily in the correct direction)? |aa|
The correct statement is:
"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"
The magnitude of the acceleration for an object can be calculated using Coulomb's law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula for the force between two charges is:
F = (k * q1 * q2) / r^2
where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.
Since the acceleration is the force divided by the mass, we can use the formula:
a = F / m
where a is the acceleration, F is the force, and m is the mass.
Given that the charge on object A is 3 times higher than on object B, and object A has a 6 times higher mass than object B, we can determine that:
The force acting on object A is 3 times greater than the force acting on object B (due to the difference in charges)
The mass of object A is 6 times greater than the mass of object B
So, the acceleration of object A is 6 times less than the acceleration of object B.
Therefore, the correct statement is:
"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"
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