# Mechanics - Velocity over Time

1. Dec 8, 2012

### golanor

1. The problem statement, all variables and given/known data
A particle is moving, through a medium in which the friction is: f = bv^2 (v is the velocity).
In t=0 the velocity is $v{0}$. There is no gravity.
Write the velocity of the particle over time.

2. Relevant equations
I used: F = ma.

3. The attempt at a solution
-f=-m*a
Solving the differential equation - v(t)=m/(b*t-m/v0)
The thing is, the mass is not known in the question.
Is there a different way of solving this?

2. Dec 8, 2012

### Staff: Mentor

Just keep m as parameter, similar to b. There is no way to get rid of it.

3. Dec 8, 2012

Thanks!

4. Dec 8, 2012

### cosmic dust

Indeed, you don't have to get rid of the mass. But the solution is not correct; it should be:

m$\dot{v}$ = - b v $\Rightarrow$ v(t) = v0 exp(-γ t )

where γ = b/m

5. Dec 8, 2012

### Staff: Mentor

Don't forget the square in the force.

6. Dec 8, 2012

### cosmic dust

Ooops... I used linear friction! Sorry, the velocity will be:

v = m v0 / (b v0 t + m)

7. Dec 8, 2012

### golanor

Which is what I wrote :)