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21 March, 13:25

A truck covers 45.0 m in 8.80 s while smoothly slowing down to final speed of 3.00 m/s. Find Its Original Speed.

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  1. 21 March, 13:31
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    7.23 m/s

    Explanation:

    From Newton's equation of motion,

    v = u + at ... Equation 1.

    Where v = final velocity, u = initial velocity, a = acceleration, t = time.

    Also,

    s = ut + 1/2at² ... Equation 2

    Where s = distance.

    Given: t = 8.8 s, s = 45.0 m.

    Substitute into equation 2

    Note: we find the value of a in terms of u

    45 = u (8.8) + 1/2a (8.8) ²

    45 = 8.8u+38.72a

    38.72a = 45 - 8.8u

    38.72a = (45-8.8u)

    a = (45-8.8u) / 38.72

    also, v = 3.00 m/s

    Substituting into equation 1

    3 = u + 8.8[ (45-8.8u) / 38.72) ]

    3 = u + (45-8.8u) / 4.4

    3*4.4 = 4.4u + 45 - 8.8u

    13.2 - 45 = 4.4u - 8.8u

    -31.8 = - 4.4u

    u = - 31.8/-4.4

    u = 7.23 m/s.

    Hence the initial velocity = 7.23 m/s
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