Mathematics: KINEMATICS Topical Past Paper Questions

A particle $P$ moves in a straight line such that after time $t$ seconds, its velocity, $v$ in m s$^{-1}$, is given by $v = e^{-3t} \sin 6t$, where $0 [2] At time $t$, $P$ has displacement $s(t)$; at time $t=0$, $s(0)=0$. (b) Find an expression for s in terms of t. (c) Find the m…

[Maximum mark: 14] A rocket is travelling in a straight line, with an initial velocity of $ 140 \, \text{m} \, \text{s}^{-1} $. It accelerates to a new velocity of $ 500 \, \text{m} \, \text{s}^{-1} $ in two stages. During the first stage its acceleration, $ a \mathrm{~m s}^{-2}…

A particle moves along a straight line so that its velocity, $ v \, \mathrm{m} \, \mathrm{s}^{-1} $, after $ t $ seconds is given by $ v(t) = 1.4^{t} - 2.7 $, for $ 0 \leq t \leq 5 $. (a) Find when the particle is at rest. (b) Find the acceleration of the particle when $t=2$. [2]…