Let k>0 be a constant. Suppose that particles P1 and P2 are moving, with velocity functions given by v1 (t) and v2(t) respectively, and that v2(t) = v1(kt). For a given interval a, b, the average velocity of particle P1 on [a, b] is equal to the average velocity of P2 on some interval [c, d]. Find c and d in terms of a and b.

Let k>0 be a constant. Suppose that particles P1 and P2 are moving, with velocity functions given by v1 (t) and v2(t) respectively, and that v2(t) = v1(kt). For a given interval a, b, the average velocity of particle P1 on [a, b] is equal to the average velocity of P2 on some interval [c, d]. Find c and d in terms of a and b.