1. The equation of motion of a particle P of a mass is given by: d² mdt² = f(r)F where is the position vector of P measured from an origin O, is a unit vector in the direction, and f(r) is a function of the distance of P from O. (a) Show that x=d, where is a constant vector. dt (b) Interpret physically the cases f(r) < 0 and f(r) > 0. (c) Interpret the results in (a) geometrically. (d) Describe how the results obtained relate the motion of the planets in our solar system. (Hints: Newton's universal law of gravitational)