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13 June, 20:31

A fugitive tries to hop a freight train traveling at a constant speed Of 4.5 m/s. Just as a empty box car passes him, the fugitive starts from rest and accelerates at a = 3.6 m/s squared to his maximum speed of 8.0 m/s. How long does it take him to catch up to the empty box car? What is the distance traveled to reach the box car?

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  1. 13 June, 22:50
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    We use the kinematics equation:

    Vf = Vi + a*t

    8 = 0 + 3.6 * t

    t=2.222s to reach 8.0 m/s

    At that time the train has moved

    4.5 m/s * 2.222s = 9.999 m

    He travelled (another kinematics equation)

    Vf^2 = Vi^2 + (2*a*d)

    (8.0) ^2 = (0) ^2 + (2 * 3.6 * d)

    d=8.888 m

    The train is 9.999m, the fugitive is 8.888m,

    He still needs to travel

    9.999-8.888 = 1.111m

    He needs to cover the rest of the distance in a smaller amount of time, however hes at his maximum velocity, so ...

    8m/s (man) - 4.5m/s (train) = 3.5 m/s more

    (1.111m) / (3.5m/s) =.317seconds more to reach the train

    So if it takes 2.222 seconds to approach the train at 8.888m, it should take

    2.222 +.317 = 2.529 seconds to reach the train completely

    Last but not least is to figure out the total distance traveled in that time frame:

    (Trains velocity) * (total time)

    (4.5m/s) * (2.529s) = 11.3805m
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