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.

Question

Nathan Hinton

Physics

16 January, 10:41

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.

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Nikhil · 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.