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

In this case, the position function is: 

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

Then, plug  into the velocity function: 

Therefore, the answer is: 

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

In this case, the position function is: 

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

Then, plug  into the velocity function: 

Therefore, the answer is: 

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

In this case, the position function is: 

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

Then, plug  into the velocity function: 

Therefore, the answer is: 

If p(t) models the position of a guitar string as a function of time, find the function which models the string's velocity.

We start with position and are asked to find velocity. This means we are going to find the first 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:

To find the velocity of the moving car, we must integrate the acceleration function to get the velocity function:

The integral was found using the following rule:

Next, we can find C using the initial condition:

Rewriting the velocity function, we get

Finally, to solve for velocity at t=0.5, we simply plug this into the function:

Average velocity is another name for slope. To find this we do:

To find velocity from acceleration, we simply take the antiderivative:

If p(t) models the position of a guitar string as a function of time, find the string's velocity when .

We start with position and are asked to find velocity. This means we are going to find the first 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:

However, we are not quite done. We need to find 

So, let's simplify. 

So our answer is -6.46

To find the velocity, take the derivative of the position function. To take the derivative, multiply the exponent by the coefficient in front of the x and then subtract one from the exponent to get: . Then set that equal to 0 to find where the velocity equals 0. .

To find the velocity function, take the derivative of the position function, which is Then, to find v(1), plug in 1 for t. Therefore your answer is: .