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24 August, 23:23

A car traveling at 45 m/s can brake to a stop within 10m. Assume that the braking force is effective for stop and constant with speed. If the car speeds up to 90 m/s, what is its stopping distance? Provide your explanation using principle of work and energy.

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  1. 25 August, 02:06
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    40 m

    Explanation:

    A car travelling at 45 ms has a kinetic energy of

    Ec = 1/2 * m * v^2

    We do not know the mass, so we can use specific kinetic energy:

    ec = 1/2 * v^2

    In this case

    ec = 1/2 * 45^2 = 1012 J/kg

    If it stops in 10 m, the braking force performed a sppecific work of 1012 J/kg in 10 m

    L = F * d

    F = L / d

    F = 1012 / 10 = 101.2 N/kg

    If the car is running at 90 m/s, the specific kinetic energy of:

    ec2 = 1/2 * 90^2 = 4050 J/kg

    With the same braking force the braking distance is:

    d2 = L2 / F

    d2 = 4050 / 101.2 = 40 m
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