Further Mathematics 9231: Linear motion under variable force Topical Past Paper Questions

A particle $P$ of mass $m$ is moving in a straight horizontal line under a variable force $m(v^{2}-ku^{2})$, where $v$ is the velocity of $P$ at time $t$, $u$ is the initial velocity of $P$, and $k$ is a positive constant. It is given that $u>0$ and $k>1$. (a) Explain why, initia…

A particle P of mass m kg is projected vertically upwards from a point O with an initial speed of $ 20 \, \text{m s}^{-1} $ and moves under gravity. There is a resistive force of magnitude $ 0.025 \, \text{mV}^2 \, \text{N} $, where $ v \, \text{m s}^{-1} $ is the speed of P at t…

A particle P of mass mkg is held at rest at a point O and released so that it moves vertically under gravity against a resistive force of magnitude $ 0.1mv^{2} $ N, where $ v_{ms}^{-1} $ is the velocity of P at time t s. (a) Find an expression for v in terms of t. The displacemen…