1. Consider an object on some trajectory r(t) and define v = r' as the velocity with speed v = |r']. (a) Show that we can write v = vT. (b) Show that we can write the acceleration as a = arT+ anN where ar and an are the tangential and normal acceleration components that are func- tions of the speed and curvature. Explain why an object with constant speed can still experience an acceleration. (c) Consider a trajectory r(t) = (t – 1,t – t³). Compute the curvature as well as the tangential and normal components of the acceleration.

1. Consider an object on some trajectory r(t) and define v = r' as the velocity with speed v = |r']. (a) Show that we can write v = vT. (b) Show that we can write the acceleration as a = arT+ anN where ar and an are the tangential and normal acceleration components that are func- tions of the speed and curvature. Explain why an object with constant speed can still experience an acceleration. (c) Consider a trajectory r(t) = (t – 1,t – t³). Compute the curvature as well as the tangential and normal components of the acceleration.