Question

A particle of unit mass moves along the x-axis under the influence of a resistive force
−kv^n i, where k is a positive constant and v is the magnitude of the velocity v at time t.
Find the times and distances at which the particle comes to rest, i.e. v = 0, for the
following cases:
(i) n < 1,
(ii) 1 < n < 2,
You may assume that at t = 0, x = 0 and v = v0