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A driver of a car going 95.0 km/h suddenly sees the lights of a barrier 39.0 m ahead. It takes the driver 0.95 s before he applies the brakes, and the average acceleration during braking is -10.0 m/s2.

What is the maximum speed at which the car could be moving and not hit the barrier 39.0 m ahead? Assume the acceleration rate doesn't change.

  • Physics -

    Ignore the 95.0 km/h speed of the driver. He may hit the barrier. They want you to calculate the speed V for which the stopping distance would be exactly 39.0 m.

    The stopping distance will be

    V*0.95 + (V/{a})*(V/2) = 39.0 m

    Solve for V.

    The second term, V^2/(2|a|)
    is the distance travelled with brakes applied, It equals the average speed times the time spent braking. The first term, V/0.95s, it the distance travelled before the brakes are applied,

  • Physics -

    Can you go through and show all work to the finish?

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