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26 September, 18:11

The acceleration of a motorcycle is given by ax (t) = at-bt2, where a=1.50m/s3 and b=0.120m/s4. the motorcycle is at rest at the origin at time t=0. calculate the maximum velocity it attains.

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  1. 26 September, 18:39
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    From given information, the acceleration is

    a (t) = 1.5t - 0.12t² m/s²

    Integrate to obtain the velocity.

    v (t) = (1/2) * 1.5t² - (1/3) * 0.12t³ + c₁

    = 0.75t² - 0.04t³ + c₁ m/s

    Because v (0) = 0 (given), therefore c₁ = 0

    The velocity is

    v (t) = 0.75t² - 0.04t³ m/

    The velocity is maximum when the acceleration is zero. That is,

    t (1.5 - 0.12t) = 0

    t = 0 or t = 1.5/.12 = 12.5 s

    Reject t = 0 because it yields zero value.

    The maximum velocity is

    v (12.5) = 0.75 * (12.5²) - 0.04 * (12.5³) = 39.0625 m/s

    Answer: The maximum velocity is 39.06 m/s (nearest hundredth)

    The graph shown below displays the velocity.
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