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28 June, 17:28

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 41m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 10 m/s2. What is the maximum speed you could have and still not hit the deer?

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  1. 28 June, 21:14
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    Maximum speed you could have and still not hit the deer = 24.07 m/s

    Explanation:

    Let the maximum speed you could have and still not hit the deer be y.

    Your reaction time before stepping on the brakes is 0.50s.

    Distance traveled during this time = 0.5y

    A deer steps onto the road 41m in front of you

    Remaining distance to deer = 41 - 0.5y

    The maximum deceleration of your car is 10 m/s²

    We have equation of motion, v² = u² + 2as

    Initial velocity, u = y m/s

    Final velocity, v = 0 m/s

    Acceleration, a = - 10 m/s²

    Displacement, s = 41 - 0.5y

    Substituting,

    v² = u² + 2as

    0² = y² + 2 x - 10 x (41 - 0.5y)

    20 (41 - 0.5y) = y²

    820 - 10 y = y²

    y² + 10 y - 820 = 0

    y = 24.07 m/s or y = - 34.06 m/s (not possible)

    Maximum speed you could have and still not hit the deer = 24.07 m/s
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