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29 January, 16:14

A car of mass 800 kg is travelling at 30 m/S. The car then brakes suddenly and stops with a braking distance of 75 m find the work done on the car by the brakes

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  1. 29 January, 16:41
    0
    -360 kJ

    Explanation:

    Given:

    m = 800 kg

    v₀ = 30 m/s

    v = 0 m/s

    Δx = 75 m

    Find: W

    We can solve this using either forces or energy.

    To use forces, first find the acceleration.

    v² = v₀² + 2aΔx

    (0 m/s) ² = (30 m/s) ² + 2a (75 m)

    a = - 6 m/s²

    Then apply Newton's second law:

    ∑F = ma

    F = (800 kg) (-6 m/s²)

    F = - 4800 N

    Work is force times distance:

    W = FΔx

    W = (-4800 N) (75 m)

    W = - 360,000 J

    W = - 360 kJ

    If you want to use energy instead:

    work = change in energy

    W = ΔKE

    W = ½mv² - ½mv₀²

    W = ½ (800 kg) (0 m/s) ² - ½ (800 kg) (30 m/s) ²

    W = - 360,000 J

    W = - 360 kJ
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