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Math Help - kinematics problem.

  1. #1
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    kinematics problem.

    rocket powered sledge accelerates at 35ms-2 and takes 1.6s to pass through a 60m section of a test track. Find the speed at which it entered the section what was its speed when it left?

    I think this is the equation to use x=ut + 1/2at2 and than use a=v-u/t to get v ?

    a= 35m/s
    t= 1.6s
    u=?
    v=?
    x= 60m




    please show your working

    thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by hana_102 View Post
    rocket powered sledge accelerates at 35ms-2 and takes 1.6s to pass through a 60m section of a test track. Find the speed at which it entered the section what was its speed when it left?

    I think this is the equation to use x=ut + 1/2at2 and than use a=v-u/t to get v ?

    a= 35m/s
    t= 1.6s
    u=?
    v=?
    x= 60m




    please show your working

    thanks
    You are correct, but let me clean this up a bit.

    Let the start of the track be your origin and let the +x direction be the direction of the acceleration.

    So as you suggested
    x = x_0 + v_0t + \frac{1}{2}at^2
    becomes
    x = v_0t + \frac{1}{2}at^2
    and gives you a v_0.

    Then v = v_0 + at
    gives your v.

    -Dan
    Last edited by topsquark; October 17th 2007 at 08:07 AM.
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  3. #3
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    When you manipulate the formula to give v it does not equal 9.5.
    u= 1/2at2 + x / t
    ??


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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by topsquark View Post
    You are correct, but let me clean this up a bit.

    Let the start of the track be your origin and let the +x direction be the direction of the acceleration.

    So as you suggested
    x = x_0 + v_0t + \frac{1}{2}at^2
    becomes
    x = v_0t + \frac{1}{2}at^2
    and gives you a v_0.

    Then v = v_0 + at
    gives your v.

    -Dan
    You forgot to divide the acceleration term by t when you solved for v, and you have some negation problems:
    u = \frac{x}{t} - \frac{1}{2}at

    Okay, let's do some numbers:
    x = 60~m
    a = 35~m/s^2
    t = 1.6~s

    So
    60 = 1.6v_0 + \frac{1}{2}(35)(1.6)^2

    Gives
    v_0 = 9.5~m/s

    and
    v = 9.5 + (35)(1.6) = 65.5~m/s

    -Dan
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