Standard +0.8 This is a standard Further Maths mechanics question requiring formation and solution of a first-order differential equation (F=ma with resistance). While it involves multiple steps (setting up equation, separating variables, integrating, applying initial conditions), it follows a well-established method taught in Further Maths courses. The 6 marks reflect the working required rather than exceptional difficulty. It's moderately harder than average A-level due to being Further Maths content, but remains a textbook-style exercise.
A particle \(Q\) of mass \(m\) kg falls from rest under gravity. The motion of \(Q\) is resisted by a force of magnitude \(mkv\) N, where \(v\) ms\(^{-1}\) is the speed of \(Q\) at time \(t\) s and \(k\) is a positive constant.
Find an expression for \(v\) in terms of \(g\), \(k\) and \(t\). [6]
A particle $Q$ of mass $m$ kg falls from rest under gravity. The motion of $Q$ is resisted by a force of magnitude $mkv$ N, where $v$ ms$^{-1}$ is the speed of $Q$ at time $t$ s and $k$ is a positive constant.
Find an expression for $v$ in terms of $g$, $k$ and $t$. [6]
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q2 [6]}}