# Homework Help: Acceleration proportional to velocity

1. Aug 31, 2010

### s0laris

1. The problem statement, all variables and given/known data
A particle is accelerated from rest with acc. proportional to velocity. After traveling 10 meters the speed is 35 m/s, find the speed after the particle traveled 20 meters. (Changed the numbers a bit from the original so the answer ppbly will not be clean.)

2. Relevant equations

a=v dv/dx possibly

3. The attempt at a solution
Sat on this one for a long, long time

2. Aug 31, 2010

### HallsofIvy

"Tanks"?

No, a is not "v dv/dx". Rather a= dv/dx which, here, is proportional to v:
a= dv/dx= kv for some number k.

From that dv/v= kdx. Now integrate both sides.

3. Aug 31, 2010

### diazona

a = dv/dt, I think you mean?

4. Aug 31, 2010

### s0laris

Yea, watch out for those advancing tanks; hah, no I meant to say thanks.
Anyway, I do believe that a= v dv/dx ; dv/dt = (dv/dx)(dx/dt) = v (dv/dx). Does this seem reasonable:
a=kv=v dv/dx
k=dv/dx
k dx = dv
intg.
v=kx
??? or is dividing by v not allowed => loss of roots or something???

5. Aug 31, 2010

### diazona

I do believe you're right, a = v dv/dx. (In one dimension of course) And I don't see anything wrong with your work.

Can you think of a reason why dividing by v would not be allowed? (hint: what number(s) are you not allowed to divide by?)