Consider a collision between two spheres where there was an elastic force acting between the two bodies. F=u*dv/dt=-h*x^3/2 where velocity v=dx/dt, h is a constant, u is the reduced mass (m1*m2/m1+m2), and x is the "change in distance" between the centers of the two bodies. Maximum compression distance is X_m, and initial velocity is v_i. Show that the collision time, t, is given by t=2(X_m)/(v_i)* [Integral from 0 to 1 of (1-k^5/2)^(-1/2) dk], where k is a dimensionless variable replaced in the integral for x. Just some idea to start this off would be much appreciated. Thanks!