# Kinematics-Motion in one dimension

## 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
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

## Homework Equations

Let
be the distance AB,
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]

Last edited by a moderator:

gneill
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.

Ray Vickson
Homework Helper
Dearly Missed

## 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
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

## Homework Equations

Let
be the distance AB,
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:
Mastermind01
Sorry for using bold font.

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..