In order to find the acceleration function from the velocity function we need to take the derivative of the velocity function 

When taking the derivative, we use the power rule which states

Applying this rule we get

As such 

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: 

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: 

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: 

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: 

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: 

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: 

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:

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

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