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

Using the product rule:

Factoring out a . 

To find the acceleration of the peach, we must take the first derivative of the velocity function:

The derivative was found using the following rule:

Now, to find the velocity at the specific t, plug in this t value into the acceleration function:

.

To find acceleration, we take two derivatives of position:

By the chain rule:

To take the derivative of this, we need the quotient rule:

At ,

If p(t) models the position of a guitar string as a function of time, find the acceleration function of the string.

We start with position and are asked to find acceleration. This means we are going to find the second derivative of p(t). 

Recall that the derivative of sine is cosine, and the derivative of a linear term is a constant.

With that in mind, we get the following:

So we get:

If p(t) models the position of a guitar string as a function of time, find the acceleration of the string when .

We start with position and are asked to find acceleration. This means we are going to find the second derivative of p(t). 

Recall that the derivative of sine is cosine, and the derivative of a linear term is a constant.

With that in mind, we get the following:

So we get:

However, we need to find 

So our answer is 

To find acceleration, you must first find the velocity function, which is the derivative of the position function. To take the derivative, multiply the exponent by the coefficient and then subtract one from the exponent: . Then, take the derivative of that to find the acceleration: .

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