# What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = 36-t^2# from #t in [2, 6]#?

##### 1 Answer

#### Explanation:

To get the average speed, we must sum the velocity and divide by the time traveled. We have a continuous function so we must integrate to sum the velocity. So average velocity is given by:

Now, we have been given the acceleration which means we must first integrate to find the formula for velocity, so:

Using the fact that the object is still at at

So we have for the velocity:

Now we can use this to get the average velocity, in our case the initial time

Now putting that into the expression for the average velocity: