Physics

A race driver has made a pit stop to refuel. After refueling, he leaves the pit area with an acceleration whose magnitude is 6.0m/s 2 . After 4.0s he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant speed of 70 m/s overtakes and passes the entering car. If the entering car maintains its acceleration, how much time is required for it to catch the other car?

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  1. Measure time from the instant the pit car (#1) enters the speedway. When that car enters, its speed is 6.0 * 4.0 = 24 m/s, and it is still accelerating.
    X1 = Vo t + (1/2) a t^2 = 24t + 3 t^2
    For the constant-speed car,
    X2 = 70 t
    The time required for car 1 to catch up with car #2 is given by
    X1 = X2
    24t + 3 t^2 = 70t
    46t = 3 t^2
    t = 0 or 46/3 s
    We are not interested in the t=0 solution, therefore
    t = 15.3 s

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