Solution to the November, 2018 Challenge Born to turn*

Consider the circular motion of the motorcycle. In order to speed up there must be a frictional force (static) acting in a direction tangent to the path. As it gets more and more speed there has to be a frictional force (static) to provide the necessary centripetal acceleration. Thus, during the acceleration phase, the total frictional force between the tires and the road has two components: one radial and one tangential. As the bike achieves maximum speed, the only component that’s left is the radial one, providing the centripetal acceleration. At all times, the frictional force should not exceed the maximum static frictional force. That means there is a maximum acceleration that the bike has: a_max. During the speeding up phase, that acceleration has 2 components: a_t – tangential, and a_r – radial/centripetal. The total acceleration is a sum of the two.

The maximum speed that...