Putnam 1946 B6

A particle moves on a circle with center $O$ , starting from rest at a point $P$ and coming to rest again at a point $Q$ , without coming to rest at any intermediate point. Prove that the acceleration vector of the particle does not vanish at any point between $P$ and $Q$ and that, at some point $R$ between $P$ and $Q$ , the acceleration vector points in along the radius $RO.$