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