Classical Mechanics (Kibble & Berkshire) · Problem 2.9

Newton's laws of motion and the law of gravitation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · polar-coordinates-motion

Problem

A bee flies on a trajectory such that its polar coordinates at time

t

are given by

r = \frac{bt}{\tau^2}(2\tau - t) \qquad \theta = \frac{t}{\tau} \qquad (0 \leq t \leq 2\tau),

where

b

and

\tau

are positive constants. Find the velocity vector of the bee at time

t

. Show that the least speed achieved by the bee is

b/\tau

. Find the acceleration of the bee at this instant.