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13 April, 14:32

Work-Energy Theorem: A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?

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  1. 13 April, 17:36
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    The same braking force does work on these objects to slow them down. The work done is equal to their change in kinetic energy:

    FΔx = 0.5mv²

    F = force, Δx = distance traveled, m = mass, v = speed

    Isolate Δx:

    Δx = 0.5mv²/F

    Calculate Δx for each object.

    Object 1: m = 4.0kg, v = 2.0m/s

    Δx = 0.5 (4.0) (2.0) ²/F = 8/F

    Object 2: m = 1.0kg, v = 4.0m/s

    Δx = 0.5 (1.0) (4.0) ²/F = 8/F

    The two objects travel the same distance before stopping.
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