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.

Answer 1

32 mph
   First, let's calculate the location of the particle at t=1, and t=4
 t=1
 s = 6*t^2 + 2*t
 s = 6*1^2 + 2*1
 s = 6 + 2
 s = 8 t = 4
 s = 6*t^2 + 2*t s = 6*4^2 + 2*4
 s = 6*16 + 8
 s = 96 + 8
 s = 104
   So the particle moved from 8 to 104 over the time period of 1 to 4 hours. And the average velocity is simply the distance moved over the time spent. So:
 avg_vel = (104-8)/(4-1) = 96/3 = 32
   And since the units were miles and hours, that means that the average speed of the particle over the interval [1,4] was 32 miles/hour, or 32 mph.