A particle moves in a straight line with velocity v ms^-1. Its initial velocity is u ms^-1. At any time t, the velocity v is given by the equation (dv/dt) + 3 + v^2=2. Prove that the particle comes instantaneously to rest after tan^-1 seconds. Given that the particle moves s metres in t seconds, show that the particle first comes to rest after a displacement of 1/2 ln (1+u^2) metres.