Question

A particle moves on a line away from its initial position so that after t hours it is s = 6t2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.

I started by taking the derivative of s(t) but am not sure how the interval fits into that. Any help or hint to solve is greatly appreciated!

Answer 1

Since you want the average velocity, you don't even need the derivative

when t = 1, s = 6(1) + 2(1) = 8
when t = 4, s = 6(16) + 2(4) = 104

average speed = total distance/total time
= (104-8)/(4-1)
= 32 mph