Mathematics 7356: Kinematics Topical Past Paper Questions

A particle moves in a straight line with acceleration $ a \, m s^{-2} $, at time t seconds, where $$ a=10-6t $$ The particle's velocity, $v$ m s$^{-1}$, and displacement, $r$ metres, are both initially zero. Show that $$ r=t^{2}(5-t) $$ Fully justify your answer.

A toy remote control speed boat is launched from one edge of a small pond and moves in a straight line across the pond's surface. The boat's velocity, $ v_{m}s^{-1} $, is modelled in terms of time, t seconds after the boat is launched, by the expression $$ v=0.9+0.16t-0.06t^{2} $…

Jermaine and his friend Meena are walking in the same direction along a straight path. Meena is walking at a constant speed of $ u \, m s^{-1} $ Jermaine is walking $ 0.2 \, m \, s^{-1} $ more slowly than Meena. (a) When Jermaine is $d$ metres behind Meena he starts to run with a…