Differential Equation question.

chris241111

A particle of mass m is projected along a smooth horizontal surface with initial speed 10m/s.
There is air resistance to motion of 1/3mv, where v is the velocity of the particle. No other forces acts on the particle. Find the velocity of the particle after 3 seconds.

A bit stuck any help appreciated

chris241111

BTW, the answer is 10/e

sdio

1. Start with the equation F=ma
2. Replace a with dv/dt
3. Separate the variables (put v's on one side and t's on other)
4. Integrate both sides with appropriate limits
5. Simplify

I hope this helps!