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Thread: show time travelled with uniform speed

  1. #1
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    show time travelled with uniform speed

    a lift starts from rest with constant acceleration 4m/s squared. it then travels with uniform speed and finally comes to rest with constant retardation 4m/s squared. the total distance travelled is D an the total time is t

    (i) show that the time for which it travelled with uniform speed is
    t squared-d
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  2. #2
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    Quote Originally Posted by ronan116 View Post
    a lift starts from rest with constant acceleration 4m/s squared. it then travels with uniform speed and finally comes to rest with constant retardation 4m/s squared. the total distance travelled is D an the total time is t

    (i) show that the time for which it travelled with uniform speed is
    t squared-d
    here is a very brief outline of an approach:

    Motion 1:
    u = 0
    a = 4 m/s^2
    $\displaystyle t = t_1$
    $\displaystyle v = v_1$
    $\displaystyle x = x_1$

    Motion 2:
    $\displaystyle x_2 = v_1 t_2$

    Motion 3: By symmetry with motion 1
    $\displaystyle u = v_1$
    a = -4 m/s^2
    $\displaystyle t = t_1$
    v = 0
    $\displaystyle x = x_1$

    Given:

    $\displaystyle t = 2 t_1 + t_2$ .... (1)

    $\displaystyle D = 2 x_1 + v_1 t_2$ .... (2)

    Use the motion data to get $\displaystyle x_1$ and $\displaystyle v_1$ in terms of $\displaystyle t_1$ and substitute into equation (2).

    Then solve equations (1) and (2) simultaneously.
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