What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) =2t^2-2t-2# from #t in [2, 3]#?
Since average speed is given by the equation
We need to find the positions of the car at times
We can derive first the velocity equation from the acceleration, and then the position from that velocity equation, via integration, and we'll assume the initial position and velocity are
Now we have our position equation,
So, the average velocity of the car on the interval