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2 December, 04:02

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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  1. 2 December, 07:26
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    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.
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