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Kinematics-Motion in one dimension

  • #1
7
1

Homework Statement


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


Homework 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]


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. [/B]
 
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Answers and Replies

  • #2
gneill
Mentor
20,792
2,770
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.
 
  • #3
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

Homework Statement


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


Homework 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]


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. [/B]
Please avoid using bold fonts; it looks like you are yelling at us.
 
Last edited by a moderator:
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Likes Mastermind01
  • #4
7
1
Sorry for using bold font.
 
  • #5
7
1
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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