physics

A speeder traveling at a constant speed of 117 km/h races past a billboard. A patrol car pursues from rest with constant acceleration of (7.6 km/h)/s until it reaches its maximum speed of 175 km/h, which it maintains until it catches up with the speeder.(a) How long does it take the patrol car to catch the speeder if it starts moving just as the speeder passes? (b) How far does each car travel?

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  1. Speeder: Vo = 117,000m/3600s = 32.5 m/s. Ds = Vo*t = 32.5*t. = Distance traveled by speeder.

    Patrol car: a = (7600m/3600s)/s = 2.11 m/s^2.

    V = 175,000m/3600s = 48.6 m/s.
    Vo = 0.

    V^2 = Vo^2 + 2a*D, Dp = V^2/2a = (48.6)^2/4.22 = 560 m = Distance traveled by patrol car.

    a. Ds = Dp, 32.5*t = 560, t =
    17.2 s. To catch up.

    b. Ds = Dp = 560 m.

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  2. Correction:
    Speeder: Vo = 117,000m/3600s = 32.5 m/s. Ds = 32.5*t = Distance traveled by speeder.

    Patrol car: a = (7600m/3600s)/s = 2.11 m/s^2.

    a. 32.5t = 0.5*2.11*t^2, 1.05t = 32.5, t = 31 s.

    b. Ds = Dp = 32.5*t = 32.5*31 = 1006 m.

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