How do you find v(t) when there is a velocity dependent force acting on the object? E.g. A car of mass 1000kg is traveling at 25 m/s. If the engine stops providing force to the car and the wind resistance is given by f=70v (v is in m/s and f is N), how long does it take for the car to reach 12.5 m/s?
I know that the acceleration should be the force/mass, so a(t)=70v/1000kg, but I don't know where to go next. Or is the equation I give for acceleration incorrect too? How should I begin?

Question

anonymous · Answer

you're on the right way , a(t)=(dv/dt)=70v/1000. Integrate it and find function for 'v' in terms of 't'. m ln(v)=70t +c , c= constant . put t=0 and v=25m/s . Find 'c'. And put the value in equation. m ln(v) = 70t + m ln(25); put v=12.5 m/s and calculate 't'.