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27 July, 11:20

A biker pedals with a constant acceleration to reach a velocity of 7.5m/s over 4.5s. During the period of acceleration, the bike's displacement is 19m. What was the initial velocity of the bike?

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  1. 27 July, 14:14
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    Given:

    v (final velocity) = 7.5 m/s

    t (time taken to pedal along) = 4.5 s

    Displacement (s) = 19 m

    Now we know that

    s=ut+1/2 (at^2)

    Where s is the displacement measured in m

    u is the initial velocity measured in m/sec

    a is the acceleration measured in m/s^2.

    t is the time taken to cover this distance.

    Substituting the given values in the above formula we get

    19 = 4.5u+1/2 (a x 4.5 x 4.5)

    20.25 a + 9 u = 38

    Now we also know that

    v = u + at

    Substituting the given values in the above formula we get

    7.5 = u + 4.5a

    Solving for u and a from the above equations we get

    u = 0.944m/s

    a = 1.45 m/s^2

    Thus the initial velocity is 0.944 m/s
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