# What is the average speed, on #t in [0,5]#, of an object that is moving at #12 m/s# at #t=0# and accelerates at a rate of #a(t) =5t^2-3t# on #t in [0,4]#?

##### 1 Answer

Given:

Initial velocity of the object

To determine the average speed for

The acceleration is given by

We know that

Separating variables,

Substituting for

Integrating both sides

At

Substituting

Thus, the expression for the velocity given by

Velocity at 4 sec is

Average velocity for the interval is

Distance travelled is obtained by integrating the expression of velocity

Separating variables,

Substituting for

Integrating both sides

Assuming the object starts from rest, s0=0

At t-4s, the position is

Total distance travelled in the interval of 4 seconds is

Total time elapsed is 4 seconds

average speed = distance /time