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Kinematics-Motion in one dimension

  1. Jun 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Two points P and Q move in a straight line AB.The point P starts from A in the direction AB with velocity 9ad99798ec4c38e165cf517cb9e02b1c9e824103.png and acceleration [PLAIN]http://latex.artofproblemsolving.com/b/b/2/bb2c93730dbb48558bb3c4738c956c4e8f816437.png.At [Broken] the same instant of time Q starts from B in the direction of A, with a velocity http://latex.artofproblemsolving.com/0/5/5/0559ffc8c62a08ff533f3fcd1a5c1713a520755d.png and acceleration [PLAIN]http://latex.artofproblemsolving.com/3/7/a/37a9e7fca70e2dce829d902af2088735306bc1a3.png.If [Broken] they pass each other at the middle point of AB and arrive at the other end of AB with equal velocities, then prove that
    1a2b273ee16fbe57397246a1713970e89d9bcbe5.png

    2. Relevant equations
    Let 859ccf4cd60c7bc6b8fa1afc9a42dc811a826d6f.png be the distance AB, 8b91b7245b0dd42b4f5585b97e323a8cfaa064a8.png be the time it takes to get midway.

    Then, [PLAIN]http://latex.artofproblemsolving.com/b/2/c/b2c07b1586491a4fe17cfa89fa189a2ae96b7aa0.png. [Broken]

    We also have [PLAIN]http://latex.artofproblemsolving.com/0/0/a/00a11d7cdd2ce508b54ea4592c254b2a6a2abc72.png.[/B] [Broken]


    3. The attempt at a solution
    I tried to do the problem by the above method but I am not getting the desired result despite many algebraic manipulations.Please can someone help me with this proof.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jun 10, 2016 #2

    gneill

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    Staff: Mentor

    Hi Googlu02, Welcome to Physics Forums.

    Consider finding separate expressions for L using both starting formulas. For the first starting point, keep in mind that L = L/2 + L/2, and that you can eliminate t1 from the result knowing that L/2 = L/2.

    Show the details of what you try.
     
  4. Jun 10, 2016 #3

    Ray Vickson

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    Science Advisor
    Homework Helper



    Please avoid using bold fonts; it looks like you are yelling at us.
     
    Last edited by a moderator: May 7, 2017
  5. Jun 10, 2016 #4
    Sorry for using bold font.
     
  6. Jun 10, 2016 #5
    Yes thank you , I got the solution.Here it is as follows:
    From the first equation we get $$t_1=\frac{2u_1-2u}{f-f_1}$$
    Now substituting the value of L in the second equation we get the desired result..
     
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