Mathematics AA: KINEMATICS, RELATIVE VELOCITY Topical Past Paper Questions

[Maximum mark:17] A particle $P$ moves in a straight line so that its displacement, $s$ cm, from a fixed point O at time $t$ seconds is given by $s(t)=2^{\left(1-\frac{t}{5}\right)}\sin\left(\frac{2\pi t}{3}\right)$, where $t\geq0$. The following diagram shows part of the graph o…

[Maximum mark: 6] A particle moves in a straight line such that its velocity, $ v \, m s^{-1} $, at time t seconds is given by $ v(t) = 1 + e^{-t} - e^{-\sin 2t} $ for $ 0 \leq t \leq 2 $. (a) Find the velocity of the particle at $t=2$. (b) Find the maximum velocity of the partic…

[Maximum mark:5] A particle moves along a straight line. Its displacement, $s$ metres, from a fixed point O after time $t$ seconds is given by $s(t)=4.3\sin(\sqrt{3t+5})$, where $0\leq t\leq10$. The particle first comes to rest after $q$ seconds. (a) Find the value of $q$. (b) Fi…