For time measured in seconds, where t is greater than or equal to zero, the velocity of a particle

For Time Measured In Seconds, Where T Is Greater Than Or Equal To Zero, The Velocity Of A Particle

Answers

Answer 1

Answer: So, to find velocity we take the first derivative of the equation.

just in case you do not know how to take a derivative or a polynomial

the derivative of axn  = naxn-1  where a is a coefficient and n is the exponent.

s' = 3t2 - 24t +36 this is your velocity in time t.

to solve for your velocity at t = 3 seconds we will plug 3 seconds into any t in the velocity equation.

s' = v this is just stating that s' is equal to your velocity

v = 3(3)2 - 24(3) + 36

v = 27 - 72 + 36

v = -9 m/s

to find when the particle is at rest we must consider the at rest velocity which is 0. An object at rest has no velocity(only applies to Newtonian mechanics)

so, we will change v to 0 and solve for t

0 = 3t2 - 24t + 36

to solve this we need to factor to quadratic equation.

to solve this we first will factor out 3 from the equation.

0 = 3(t2 - 8t + 12)

now we can factor. we need two numbers that when multiplied together give 12 but when added give -8. since the addition is negative and the multiplication is positive we know that we are dealing with two negative integers.

we end up with

0 = (t-2)(t-6)   the three was divided on both sides to eliminate it from the equation.

so, the particle is at 0 at t = 2 seconds and t = 6 seconds.

Now, just because the particle has 0 velocity does not mean it has no acceleration. However, I do not believe the acceleration is important for this problem.

To find when the particle is moving forward you must consider again when it is at 0. When it is at 0 a speed change is happening. So, to find out if velocity is positive or negative we will test a number before 2 after 2 but before 6 and after 6.

So, we can start with t = 0 for the before 2 number

v = 3(0) - 24(0) + 36

we get v = 36 which is positive. So, the particle was moving forward before 2 seconds.

now we have already used 3 seconds and we got a negative velocity. So, the particle is moving backwards at t = 3 seconds.

So the last one to check is after 6 seconds. We will choose 10 for this one because it is easy to multiply with.

v = 300 - 120 + 36 = a positive number. You do not actually need to know what number as long as you know it is positive. That means the particle was moving forward after 6 seconds.

to find the total distance traveled we must break up the distance equation by direction of travel. So, we must take the distance traveled by the particle in pieces using the original equation.

s = t3 -12t2 + 36t

first we will solve for the distance traveled in 2 seconds.

s = 8 - 48 + 72 = 32 meters

Now we will solve for 6 seconds and figure out the distance traveled from 32 meters in the opposite direction. Then we will add the two numbers together.

s =216 - 432 + 192 = -24 meters

To find the distance travelled between 2 and 6 seconds we add the absolute value of the values together.

We end up with distance traveled between 2 and 6 seconds was

56 meters

we then add this to the original 24 meters to get the distance traveled from 0 to 6 seconds of

88 meters

then we solve for the distance at 8 seconds

s = 512 - 768 + 288 = 32 meters

so, again we add the absolute values of the previous time interval with the one we just calculated for.

24 + 32 = 56 meters. So, the particle traveled back up at this point.

We add the new 56 with the current total of 88 meters to get

total distance traveled  = 144 meters

this shows us that the particle is moving in a wave pattern from 0 to 8 seconds. So, if you were to draw a graph you would have a particle start at s = 0 and t = 0, then the particle would move much like the graph of sine instead of stopping at 1 it would stop at s = 32 then drop down to s = -24 and rise up continuously after that.

Step-by-step explanation:


Related Questions

Tanya's father travels every week for business. He has traveled around the
world many times. Over the past 10 years, he has accumulated approximately
460,000 frequent flyer miles. How is that number expressed in scientific
notation?
A. 4.6 × 103
B. 4.6 × 10 ​​​​​​​4
C. 4.6 × 10 5
D. 46 × 10 ​​​​​​​5

Answers

The correct answer would be: 4.6 x 10^5

The volume of a square pyramid with a height of 12m is 100 m find the Length of the square base.

Answers

Volume of square Pyramid = a^2 * h/3
If we rearrange that equation to give a (length of square base)

a = (sqrt(3)* sqrt(V))/sqrt(h)
a = (sqrt(3)* sqrt(100))/sqrt(12)
a = 5m

The difference of x and a number is 6. What is the other number?

Answers

Answer:

Answer: The other number is y = x + 6.

Step-by-step explanation:

What is p(x)? I need help ASAP

Answers

Answer:

Option C

Step-by-step explanation:

you just subtract the functions from each other.

hence,

15x - 7x - 20

p(x) = 8x - 20

Which of the following expressions are equivalent to -2(5 – 3)?
Choose all answers that apply:
A
-10 - 6
B
-10 + 6
None of the above
Peno
Sos

Answers

Answer:

It's B

-10 + 6

Step-by-step explanation:

Here, we gotta use the distributive property.

the -2 will distribute to the 5, which will make the -10

then, the -2 will also distribute to the -3 (the minus is the negative) which will make the 6

So, that should give you the -10 + 6, which is B

hope this helped :)

Answer:

[tex]\boxed{\sf{B.-10+6}}[/tex]

Step-by-step explanation:

Use the distributive property.

Distributive property:

→ A(B+C)=AB+AC

→ -2(5-3)

Multiply.

→ -2*5=-10

→ -2*3=-6

Rewrite the problem down.

→ = -10+6

Therefore, the correct answer is B. -10+6.

I hope this helps you! Let me know if my answer is wrong or not.

Linear Sequences
Please help with this question
Put either a,b,c,d
It is on linear sequences
35 points up for grabs

Answers

Answer:

please help the question

Step-by-step explanation:

How tall is this building?

Answers

Answer:

The building is 86.6 m tall.

Step-by-step explanation:

Coh Cah Toa

Coh: sin(theta) = Opp/Hyp

Cah: cos(theta) = Adj/Hyp

Toa: tan(theta) = Opp/Adj

Using Toa.

tan(theta) = Opp/Adj

tan(60°) = x/50

x = 50 * tan(60°)

x = 50 * √(3)

x ≈ 86.60254038

x = 86.6 m

Please help me with algebra question will mark brainliest to first person with a real answer

Answers

Answer:

367/90

Step-by-step explanation:

As [tex]4.\bar{7}=4\frac{7}{9}[/tex], this means that [tex]0.4\bar{7}=4\frac{7}{90}=\frac{367}{90}[/tex], 1/10th of 4.7 repeated.

What’s the scale factor? Quick

This is on ixl and I have to get at least a 90

Answers

Answer:

4

Step-by-step explanation:

We start with the smaller shape. We look at each coordinate and we multiply by 4. That will give us the coordinates for the bigger shape.

if a-1/a=5 then find the value of a square +1/asquare​

Answers

Answer:

3

Step-by-step explanation:

Calculating a

a - 1 / a = 5a - 1 = 5a4a = -1a = -1/4

Substitute in the 2nd equation

a² + 1 / a²(-1/4)² + 1 / (-1/4)²1/2 + 1 / 1/23/2 / 1/23

5. Cole worked for a concrete company last weekend. On Saturday, his gross income was $350
and his net income was $307.05. On Sunday, his gross income was $280 and his net income
was $246.35. What amount did Cole pay in payroll tax last weekend?

Answers

The answer is Coles pay $76.6o in payroll tax last weekend.

PLS HELP ASAP a wheel makes 13 revolutions to cover a distance of 65 m find the radius of the wheel

Answers

Revolutions=13Distance=65m

Circumference:-

65/135m

Radius:-

2πr=5πr=2.5r=2.5/πr=0.797m

Answer:

radius = 0.8 m (nearest tenth)

Step-by-step explanation:

One revolution of the wheel means one complete turn.  Therefore, the distance of one revolution is the circumference of the wheel.

First, find the distance of one revolution (the circumference) by dividing the total distance by the given number of revolutions:

[tex]\sf circumference=\dfrac{65}{13}=5\:m[/tex]

Formula

[tex]\textsf{circumference of a circle}=\sf 2 \pi r \quad \textsf{(where r is the radius)}[/tex]

[tex]\implies \sf radius=\dfrac{circumference}{2 \pi}[/tex]

Substituting the found value of the circumference into the formula to find the radius:

[tex]\implies \sf radius=\dfrac{5}{2 \pi}=0.8\:m\:(nearest\:tenth)[/tex]

A car traveled 1010 miles at an average speed of 3030 miles per hour
and then traveled the next 1010 miles at an average speed of 5050 miles
per hour. What was the average speed, in miles per hour, of the car for the
2020 miles?

Answers

The average speed, in miles per hour, of the car for the 20 miles is 37.5 mph

Average speed

Average speed v = d/t where

d = total distance and t = total time

Making t subject of the formula, we have

t = d/v

Time to cover first 10 miles

Now when the car travels 10 miles at an average speed of 30 miles per hour,

d = 10 mi and v = 30 mph.

So, t = d/v

= 10/30

= 1/3 h

Time to cover next 10 miles

Also, when the car travels the next 10 miles at an average speed of 50 miles per hour,

d' = 10 mi and v' = 50 mph.

So, t' = d'/v'

= 10/50

= 1/5 h

Time to cover 20 miles

The total time for the 20 miles is T = t + t'

= 1/3 h + 1/5 h

= (5 + 3)/15 h

= 8/15 h

Average speed for 20 miles

So, the average speed for the 20 miles is v = D/T where

D = 20 miles and T = 8/15 h.

So, v = D/T

v = 20 mi ÷ 8/15 h

v = 20 × 15 mi/8 h

v = 2.5 × 15 mi/h

v = 37.5 mph

So, the average speed, in miles per hour, of the car for the 20 miles is 37.5 mph

Learn more about average speed here:

https://brainly.com/question/24739297

can someone help me with this question

Answers

Answer:

(4,2)

Step-by-step explanation:

It's parallel, so all of them have to be on the same way.

The last point has to be at the same distance from the one right above it

Answer:

C. (4, 2)

Step-by-step explanation:

(x, y)

if you put the last dot on (4, 2) and connected all of them, it would create a perfect parallelogram

What is the slope of the line through the points (-2, -1) and (4, 3)?


2/5

5/2

3/2

2/3

Answers

Answer:

2/3

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

   = ( 3- -1)/ ( 4 - -2)

   = ( 3+1)/ ( 4+2)

   = 4/6

   = 2/3

[tex]\huge\text{Hey there!}[/tex]


[tex]\large\textsf{The formula for slope of a line is: }\large\boxed{\mathsf{m = \dfrac{y_2 - y_1}{x_2 - x_1} \ or\ easier \ way\ m = \dfrac{rise}{run}}}[/tex]


[tex]\large\textsf{NOW LETS ANSWER THE GIVEN EQUATION}[/tex]

[tex]\large\text{THE GIVEN EQUATION: \boxed{\rm{m = \dfrac{3 - (-1)}{4 - (-2)}}}}\\\large\boxed{m \rm{= \dfrac{3 + 1}{4 + 2}}}\\\\\\\large\boxed{m \rm{= \dfrac{4}{6}}}\\\\\\\large\boxed{m \rm{= \dfrac{4\div 2}{6\div 2}}}\\\\\\\large\boxed{m = \rm{\dfrac{2}{3}}}\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ D. \dfrac{2}{3}}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]

Xaviera went out to play soccer at 5:31 and returned home at 7:00 how long was she playing soccer

Answers

Step-by-step explanation:

she played for about 1 hour 29 minutes

Answer:

1 hour and 29 minutes or 89 minutes

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

See picture for full problem. Please and thank you so very much!

Answers

Answer:

Step-by-step explanation:

i need help with this quick pls , please solve 5a​

Answers

Answer:

Step-by-step explanation:

If you use de morgan's laws to write out [tex]-(PvQ)[/tex], it returns -P ^ -Q

And if ^ means 'and', it is showing that (P and Q) and (-P and -Q) which isn't possible since there can't be something that is both true and false. Therefore, it is a contradiction since something can not be true a nd false at the same time.

Do number 2 please. Please bots don’t answer! I just trying to get help :(

Answers

Answer:

no 2. cube a' will be smaller because it was multiplied by a fraction

no 3. c

65 brainleiest! Can someone help?!

Answers

Answer:

m∡EFG = 139°, and m∡ IFH = 49°

Step-by-step explanation:

We know that vertical angles are congruent so we can say that

∡EFG ≅∡DFH and that ∡EFD≅∡GFH

Congruent angles have the same measure therefore

∡EFG = ∡DFH  = 6x+25 and

∡EFD = ∡GFH = 2x+3

Use that all those angles add up to 360° to find x

∡EFG +∡GFH +∡DFH + ∡EFD = 360°, substitute the given measures

6x+25 +2x+3 + 6x+25 +2x+ 3 = 360 , combine like terms

16x + 56 = 360, subtract 56 from both sides

16x = 304, divide both sides by 16

x = 19

m∡EFG = 6x +25 , substitute x with 19 and calculate

m∡EFG = 6·19 +25

m∡EFG = 139°

m∡ IFH = 90°- m∡GFH, substitute m∡GFH with 2x+3

m∡ IFH = 90°- (2x +3), substitute x with 19

m∡ IFH = 90°- (2·19 +3)

m∡ IFH = 90°- 41

m∡ IFH = 49°

What is the area of the shape?

Answers

Answer:12 units^2

Step-by-step explanation:

2*2=4

2*2*1/2=2

2*6*1/2=6

4+2+6=12

12 units^2

Use the picture I provided to help me answer the question.

Answers

B


Cuz there is 9 flutes and 4 violas and 9 is greater than 4

The wheel of a bike has a diameter of 26 inches. What is the circumference of the wheel?

Answers

Answer:

C ≈81.64 inches

Step-by-step explanation:

Formula : C ≈ πd

Where:

C = circumference

π ≈ 3.14 {About}

d = diameter

As Given :

Wheel of a bike has a diameter of 26 inches.

Solution:

Note - Given that diameter = 26

π ≈ 3.14 {About}

C ≈ 3.14 (26)

C ≈ 81.64

Therefore the circumference of the wheel is 81.64 inches

Kavinsky

is 627 divisible by 3

Answers

Answer:

yes.

Step-by-step explanation:

If you divide 627 by 3, you get 209 which is a whole number.

Hope this helped! Have a nice day!
Please give Brainliest when you can!

-Jaron

Answer:

technically speaking, yes. but if you don't want any remainders, (or decimals) then no.

Step-by-step explanation:

7 isnt divisable by anything, unless you have remanders or decimals, fractions ext. so yeah.

A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic centimeter?

Answers

The approximate surface area of the balloon is 199 cm².

The approximate volume of the balloon is 262 cm³

What is the surface area and the volume of the balloon?

Radius of the balloon = circumference / 6.2832

25 / 6.2832 = 3.98cm

Surface area = 4πr²

4 x 22/7 x 3.97² = 199 cm²

Volume =  4/3πr³

4/3 x 22/7 x 3.97³ = 262.20 cm³

To learn more about the volume of a sphere, please check: https://brainly.com/question/13705125

Pleaseeeeee helppp!!!!! Will mark brainliest!!

Answers

Answer:

the first one (3x-2)(2x-3)

The answer is 1,2 and 5 are factored
4 is not factored because it can be factored by y

Compare using >, < or =
7 x 5/4 _ 7
How do you know your answer is correct?
Choose 1 answer:
A. Because we are multiplying 7 by a fraction that is less than 1.
B. Because we are multiplying 7 by a fraction that is equal to 1
C. Because we are multiplying 7 by a fraction that is greater than 1.

Answers

I think the answer will be:

C but i not that sure

Answer:

C. Because we are multiplying 7 by a fraction that is greater than 1.

Step-by-step explanation:

- Sumin -

What is the measure of the unknown angle?
A 72°
B 74°
C 76°
D 79°

Answers

Answer:

C. 76 degrees.

Step-by-step explanation:

n = 180 - 104

= 76.

Answer:

C

Step-by-step explanation:

a straight line is 180 degrees

so we can say that n is equal to 180 - 104

n is equal to 76 degrees

If you can help me with this please and thank you

Answers

Answer:

Nnnnnnnnnnnn

Step-by-step explanation:

L bozo

Does anybody know this ?

Answers

Answer:

0, 1, 2, 3, 4

Step-by-step explanation:

Multiply each x value by 1/3 then add 2. Since the numerator is 1, you would multipy by one and divide by the denominator of 3, so you really need to divide each x value by 3 then add 2.

-6:

-6/3 = -2

-2 + 2 = 0

-3:

-3/3 = -1

-1 + 2 = 1

0:

0/3 = 0

0 + 2 = 2

3:

3/3 = 1

1 +2 = 3

6:

6/3 = 2

2 + 2 =4

Other Questions
Question 6 (2 points) If 100.0 mL ethyl alcohol weighs 78.5 g, determine the volume in litres occupied by 1.59 kg of ethyl alcohol. Answer Instructions: how was Nepal named on the basis of race What role did the United States play in global economicsduring the 1990s? IS What Is the effect of the structure inthe essay "Lonellness.. . an American Malady" by Carson McCullers?O A. The clear and concise narration allows the reader to draw connections acrossthe essay. B.The stream-of-consciousness narrationallows a more intimate connection to the reader. C.The melancholic thoughts in the narration create a frustrated and incoherent mood. D. The sense of moral isolation creates a need to belong among emotionally detached readers. Identifying Cause and Effect What was the NorthAtlantic Treaty Organization? Why was it formed?2 Summarizing What events led to the Berlin Airlin?How did the Soviets react?3 Explaining Why did Khrushchev support thebuilding of the Berlin Wall? Describe the militaryenforcement at the wall, PLEASE HURRY!!!!!!!Which of these does not use ribbed vaulting in its design? a. St. Etienne b. Durham Cathedral c. St. Patricks Cathedral d. All of the above use ribbed vaulting. Complete and balance the following equation K+H2O Exercise Some of the following sentonces are vaguo, 'ompty,' awkward phrases, or contorted. Rewrite each one so that it is clear and specifie, combining or dividing sentences as necessary. 1. Roger was an awesome guy who was really an important part of his company. 2. There's a new detective show on television. It stars Phil Noir and is set in the 1940s. 3. Sarah's room was always a huge disaster. 4 What is implied by the movement of people that Tap dance A.)12 B.) 25C.)51D.) 77 Suppose that you have been hired at an annual salary of $16,000 and expect to receive annual increase of 3%. What will your salary be when you begin your sixth year? Use the properties of seawater to describe the characteristics of mixtures. Why is this action surprising?You like playing games about theocean.You let your friends choose whichgame to play.You are playing a game thatsounds stressful. What is a verb? Explain by giving example BRAINLIEST TO CORRECT ANSWER!!!!PLEASE HURRY!!Which statement describes seafloor spreading? A. Deep trenches form where an oceanic plate is forced under a continent at a convergent boundary. B. Deep trenches form between two plates that are moving away from each other at a divergent boundary. C. Ocean basins grow narrower as one plate is forced downward at a convergent boundary. D. Ocean basins grow wider as new oceanic crust forms at a divergent boundary. Can yall help with this? Thanks Please help me with this please and thank you Do you think that the song version of the piece affects the meaning and overall feeling of the piece? How? annabel lee Edgar Allan Poe Please Help!Jackson has a cube. Each edge of the cube is 5 centimeters long.After the paint dries, Jackson cuts the cube in half. He makes the cut along the diagonal of one pair ofparallel faces. Rounded to the nearest thousandth, the diagonal has a length of 7.071 centimeters. Oncethe cut is made, Jackson has two identical triangular prisms.What is the combined area, in square centimeters, of the surfaces of the two prisms that were not painted? why isnt tv good for children & people write 4-5 sentences IN FRENCH.