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29 January, 08:17

A particle moves along the x-axis so that at time t its position is given by s (t) = (t + 1) (t - 3) 3, t > 0. For what values of t is the velocity of the particle increasing? a. 0 0d. The velocity is never decreasing.

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  1. 29 January, 11:55
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    Answer: d. the velocity is never decreasing.

    Therefore the velocity of the particle keeps increasing at a constant rate.

    Since the velocity function is a Linear equation with a positive slope, the velocity is never decreasing.

    Explanation:

    Given;

    The position function s (t) is given as;

    s (t) = (t+1) (t-3) 3 = 3t^2 - 6t - 9

    Velocity = change in position/change in time = ds/dt

    ds/dt = differentiating the position function

    ds/dt = 6t - 6

    v (t) = ds/dt = 6t - 6

    At t=0

    v (t) = - 6

    At t=1

    v (t) = 0

    At t=2

    v (t) = 6

    Acceleration = dv/dt = 6

    Therefore the velocity of the particle keeps increasing at a constant acceleration of 6.

    Since the velocity function is a Linear equation with a positive slope, the velocity is never decreasing.
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