Kinematics-Motion in one dimension

[Googlu02]

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]

 

[gneill]

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 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.

 

[Googlu02]

Sorry for using bold font.

 

[Googlu02]

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..