1. The problem statement, all variables and given/known data A particle moving on a straight line is subject to a resistive force of the magnitude kv^n, where v is the velocity at time t and k is a positive real constant. Find the times and distances at which the particle comes to rest i.e. v=0, for the following cases (this assumes at t=0, x=0, v=v0.) n<1 ? 1<n<2 ? n=2 ? 2. Relevant equations F=ma 3. The attempt at a solution I've tried by getting two equations, one for time and one for distance. So I set F=ma= m(dv/dt) = -kv^n for time and F = ma = mv(dv/dx) = -kv^n for distance I then plodded along, and took v=0 to get two similar equations for time and distance... (m*v0^(1-n)) / (k (1-n)) = t and (m*v0^(2-n)) / (k (2-n)) = x but I'm not sure if that's at all right! They'd be fine for n<1, but the time one screws up for 1<n<2 and the distance is special for n=2. Basically I'm not sure I've gone the right way at all... I think I need an e^f(t) so I can take limits but I've just got my head in a muddle.