Calculus 1 : How to find acceleration

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #321 : Acceleration

The position of  is given by the following function: 

Find the acceleration.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then take the derivative of the velocity function to get the acceleration function: 

Then, plug 

 into the acceleration function: 

Therefore, the answer is: 

Example Question #322 : Acceleration

The position of  is given by the following function: 

Find the acceleration.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then take the derivative of the velocity function to get the acceleration function: 

Then, plug  into the acceleration function: 

Therefore, the answer is: 

Example Question #323 : Acceleration

The position of  is given by the following function: 

Find the acceleration.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then take the derivative of the velocity function to get the acceleration function: 

Then, plug  into the acceleration function: 

Therefore, the answer is: 

Example Question #324 : Acceleration

The position of  is given by the following function: 

Find the acceleration.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then take the derivative of the velocity function to get the acceleration function: 

Then, plug  into the acceleration function: 

Therefore, the answer is: 

Example Question #325 : Acceleration

The position of  is given by the following function: 

Find the acceleration.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then take the derivative of the velocity function to get the acceleration function: 

Then, plug  into the acceleration function: 

Therefore, the answer is: 

Example Question #326 : Acceleration

The position of  is given by the following function: 

Find the acceleration.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function. Then find the derivative of the velocity function to get the acceleration function: 

In this case, the position function is: 

Then take the derivative of the position function to get the velocity function: 

Then take the derivative of the velocity function to get the acceleration function: 

Then, plug  into the acceleration function: 

Therefore, the answer is: 

Example Question #327 : Acceleration

If v(t) is a function which models the velocity of a wave as a function of time, find the function which models the wave's acceleration.

Possible Answers:

Correct answer:

Explanation:

If v(t) is a function which models the velocity of a wave as a function of time, find the function which models the wave's acceleration.

We are given velocity and asked to find acceleration. To do so, we need to find the derivative of our velocity function.

Recall that the derivative of cosine is negative sine, and that the derivative of any variable can be found by multiplying the term by the exponent and reducing the exponent by one.

So we have:

Example Question #328 : Acceleration

If v(t) is a function which models the velocity of a wave as a function of time, find the the wave's acceleration when t=0.

Possible Answers:

Correct answer:

Explanation:

If v(t) is a function which models the velocity of a wave as a function of time, find the the wave's acceleration when t=0.

We are given velocity and asked to find acceleration. To do so, we need to find the derivative of our velocity function.

Recall that the derivative of cosine is negative sine, and that the derivative of any variable can be found by multiplying the term by the exponent and reducing the exponent by one.

So we have:

We are not quite done yet however. We need to find a(0)

So our answer is -5

Example Question #329 : Acceleration

What is the instantaneous acceleration at time t = 25 of a particle whose positional equation is represented by s(t) = –44t2 + 70√t?

Possible Answers:

–2193

–88.82

–1328

None of the other answers

97.39

Correct answer:

–88.82

Explanation:

The instantaneous acceleration is represented by the second derivative of the positional equation. Let's first calculate the velocity then the acceleration. Begin by rewriting s(t) to make the differentiation easier:

s(t) = –44t2 + 70√t = –44t2 + 70(t)1/2

v(t) = s'(t) = –88t + 70 * (1/2) * t–1/2 = –88t + 35t–1/2

a(t) = v'(t) = s''(t) = –88 - 70t–3/2 = –88 -70/(t√t)

a(5) = –88 -70/(25√25) = -88 - 70/(5 * 5) = –88 - 70/25 = –88.82

 

Example Question #721 : Spatial Calculus

Find the acceleration function of a particle who's velocity is given by:

Possible Answers:

Correct answer:

Explanation:

To find acceleration we simply take the first derivative of velocity with respect to time:

Using the product rule:

Factoring out a 

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