Mechanics - Velocity over Time

[golanor]

Homework Statement

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.

Homework Equations

I used: F = ma.

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?

 

[mfb]

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

 

[golanor]

Thanks!

 

[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

 

[mfb]

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

Don't forget the square in the force.

 

[cosmic dust]

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

v = m v₀ / (b v₀ t + m)

 

[golanor]

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

v = m v₀ / (b v₀ t + m)

Which is what I wrote :)