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Math Help - Kinematics-Constant Acceleration

  1. #1
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    Kinematics-Constant Acceleration

    I do not understand how the question can be solved if I have only been given the times and distances. I thought that you need 3 items.

    There are two items to work out so how do I do this with only the distance and time:
    P, Q and R are three points on a straight road, such that PQ=184m and QR=285.75m . A car traveling with constant deceleration passed points P, Q and R at times t=0, t=8 and t=25 seconds respectively. What is the retardation and the velocity of the car at P.

    I know the equations for constant acceleration are:
    v=u+at
    v^2=u^2+2as
    s=0.5(u+v)t
    s=ut+0.5 * a * t^2

    I tried working out the velocity using distance divided by time but this is average and not useful. I then tried rearranging the equation so a was the subject and then put the two equal to each other which did not work.
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  2. #2
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    Quote Originally Posted by aqua View Post
    I do not understand how the question can be solved if I have only been given the times and distances. I thought that you need 3 items.

    There are two items to work out so how do I do this with only the distance and time:
    P, Q and R are three points on a straight road, such that PQ=184m and QR=285.75m . A car traveling with constant deceleration passed points P, Q and R at times t=0, t=8 and t=25 seconds respectively. What is the retardation and the velocity of the car at P.

    I know the equations for constant acceleration are:
    v=u+at
    v^2=u^2+2as
    s=0.5(u+v)t
    s=ut+0.5 * a * t^2

    I tried working out the velocity using distance divided by time but this is average and not useful. I then tried rearranging the equation so a was the subject and then put the two equal to each other which did not work.
    Using the kinematic equations gives

    \displaystyle x=x_0+v_0t+\frac{a}{2}t^2

    you can start at the origin this gives x_0=0

    Now you know two other points (x,t) that is
    (184,8) and (469.75,25)

    This gives the system of equations
    \begin{array}{rcrcr} 8v_0 & +&32a & =&184 \\ 25v_0 & +& \frac{625}{2}a& =& 469.75\end{array}

    Can you finish from here
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