7. A particle is moving along a straight line so that its velocity at time t ³ 0 is v(t) = 3t2. At what time t during the interval from t = 0 to t = 9 is its velocity the same as the average velocity over the entire interval?

 

A. 3

B. 4.5

C. 3(3)1/2

D. 9/2 (2)1/2

E. 9(3)1/2

 

 

Solution: The answer is A

 

The average of a function over an interval is the integral of the function divided by the length of the interval. So the velocity over the entire interval is given by,

 

 

Equate V(t) with the average velocity and solve for t, as follows,