# How to derive the velocity addition formula

1. Oct 1, 2012

### DODGEVIPER13

1. The problem statement, all variables and given/known data
Derive the formula v= (v'+u)/(1+v'u/c^2) the velcoty addition formula using the below formulas?

2. Relevant equations
1. vt1=L+ut1
2. (proper time)=(proper length)/v'+(proper length)/c
3. ct2=L-ut2
4. (dilated time)= (proper time)/(sqrt(1-v^2/c^2))
5. L=(proper length)sqrt(1-v^2/c^2)

3. The attempt at a solution
Ok so here is what I did I solved equation 1 above for t1 and got t1=(L+ut1)/v and equation 3 for t2 and got t2=(L-ut2)/c. I then added them together to get (dilated time or delta t)=(L+ut1)/v+(L-ut2)/c. Then I used equation 4 to get ((L+ut1)/v+(L-ut2)/c)sqrt(1-v^2/c^2)=(proper time). Then I set that equal ti equation 2 ((L+ut1)/v+(L-ut2)/c)sqrt(1-v^2/c^2)= (proper length)/v'+(proper length)/c. Then (proper length)=L/sqrt(1-v^2/c^2) and this is where I get lost in my algebra I cant seem to get rid of L and (proper length) in order to find the correct formula?

2. Oct 1, 2012

### DODGEVIPER13

whoops I think I caught some of my errors when I solved for t1 and t2 I forgot the other side?

3. Oct 1, 2012

### DODGEVIPER13

ok after reworking a bit I am still lost but 1 step closer I think. (Proper length)/v'+(proper length)/c=sqrt(1-v^2/c^2)(L/(c+u)+L/(v-u)) I have then tried using the length contraction on this but it gets very complicated uggg.

4. Oct 2, 2012

### DODGEVIPER13

Is it too confusing, should I resubmit