# What is the average speed of an object that is moving at #25 m/s# at #t=0# and accelerates at a rate of #a(t) =2-2t^2# on #t in [0,5]#?

##### 1 Answer

#### Answer:

#### Explanation:

NOTE: I am using the given a(t) as the acceleration term. Dimensionally, that doesn’t look quite right

**Average Velocity**

where

**Final Velocity**

where

t = time taken (s)

In this case:

It is moving backwards, as indicated by the negative acceleration relative to the starting point. It initially had a forward direction, so it changed direction as well as velocity.

The average velocity is thus:

This positive value just means that at time (5) it has not yet quite reached the location it was at at time (0). On average it only moved 1 meter over the time span and is now heading back.