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Math Help - Speed-Time Graph

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    Speed-Time Graph

    A cyclist starting from rest accelerates uniformly to his maximum speed of 12m/s, which he then maintains for the next 3.6 km. He then applies his brakes and decelerates to rest at a rate numerically equal to three times his acceleration. Sketch a speed-time graph and find the total time the cyclist is in motion if the total distnace moved is 3744 m.
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    Re: Speed-Time Graph

    Quote Originally Posted by Ilsa View Post
    A cyclist starting from rest accelerates uniformly to his maximum speed of 12m/s, which he then maintains for the next 3.6 km. He then applies his brakes and decelerates to rest at a rate numerically equal to three times his acceleration. Sketch a speed-time graph and find the total time the cyclist is in motion if the total distnace moved is 3744 m.

    make a sketch?

    for the first " t " seconds ...

    v_0 = 0 , v_f = 12 , let acceleration = a

    during the constant speed, you know speed and distance ... calculate the time.

    for the last " t/3 " seconds (why t/3 ???) ... acceleration = 3a , v_0 = 12 , v_f = 0

    finally, distance speeding up + distance slowing down = 144 m

    solve for t and sum up all the times.

    I get total time = 324 sec
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