A particle of mass m moves in a damping medium under the influence of a force equal to mk(v3 + c2v). where k and c are constants. (a) [1 point] Write down Newton's second law for the particle (b) [3.5 points] Find the position of the paricle as a function of time and show that for any value of the initial velocity, the particle will never make a displacement greater than 2kc (c) [3.5 points] Find the time required to reach the velocity v and show that the particle comes to rest only for t o. dx Useful integral: I = xo x2 +c2 tan - =