Acceleration proportional to velocity

[s0laris]

Homework Statement

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.)

Homework Equations

a=v dv/dx possibly

The Attempt at a Solution

Sat on this one for a long, long time

Tanks in advance

 

[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.

 

[diazona]

a = dv/dt, I think you mean?

 

[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?

 

[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?)