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16 January, 04:13

A car traveling 56.0 km/h is 24.0 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.00 s later. (a) What is the magnitude of the car's constant acceleration before impact? (b) How fast is the car traveling at impact?

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  1. 16 January, 04:27
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    Answer: (A) acceleration = - 3.6m/s². This is deceleration or negative acceleration.

    (B) Therefore, velocity just before impact, v = 8.4m/s

    Explanation:

    (a) Initial velocity, u = 56km/h = (56*1000/3600) m/s = 15.6m/s

    Distance, s = 24.0m, time, t = 2.0s, acceleration, a = ?

    Using the equation, s = ut + 1/2at²

    24.0m = 15.6m/s * 2s + (a * 2²) / 2

    24.0 = 31.2 + 2a

    2a = - 31.2 + 24

    2a = - 7.2

    a = - 7.2/2

    acceleration = - 3.6m/s². This is deceleration or negative acceleration.

    (b) final velocity just before impact, v = ? initial velocity, u = 15.6m/s, acceleration = - 3.6m/s², time, t = 2.0s

    using the equation v = u + at

    v = 15.6m/s + (-3.6m/s² * 2s)

    v = 15.6m/s - 7.2m/s

    v = 8.4m/s

    Therefore, velocity just before impact, v = 8.4m/s
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