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]#?
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: