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29 April, 12:07

A driver is moving at 17.0 m/s when she sees a child on a bike 65m ahead of her. If the car can brake at 4.9 m/s2 and the drivers reaction time is 1.6 s, can she avoid hitting the child

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  1. 29 April, 15:55
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    First, find the distance she travels before reacting:

    Δx = v₀ t + ½ at²

    Δx = (17.0 m/s) (1.6 s) + ½ (0 m/s²) (1.6 s) ²

    Δx = 27.2 m

    Now find the distance she travels before stopping:

    v² = v₀² + 2aΔx

    (0 m/s) ² = (17.0 m/s) ² + 2 (-4.9 m/s²) Δx

    Δx = 29.5 m

    The total distance traveled is:

    27.2 m + 29.5 m = 56.7 m

    56.7 m is less than 65 m, so yes, she can avoid hitting the child.
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