Moderate -0.3 This is a standard M4 differential equation problem requiring separation of variables and integration. While it involves setting up F=ma with velocity-dependent resistance, the mathematical steps are routine for this module: m(dv/dt) = -4v leads directly to separable form, integrate to get ln(v), and apply initial conditions. The 6 marks reflect multiple steps rather than conceptual difficulty—this is a textbook exercise testing core technique without requiring problem-solving insight.
A particle \(P\) of mass 2 kg moves in a straight line along a smooth horizontal plane. The only horizontal force acting on \(P\) is a resistance of magnitude \(4v\) N, where \(v\) m s\(^{-1}\) is its speed. At time \(t = 0\) s, \(P\) has a speed of 5 m s\(^{-1}\). Find \(v\) in terms of \(t\).
[6]
A particle $P$ of mass 2 kg moves in a straight line along a smooth horizontal plane. The only horizontal force acting on $P$ is a resistance of magnitude $4v$ N, where $v$ m s$^{-1}$ is its speed. At time $t = 0$ s, $P$ has a speed of 5 m s$^{-1}$. Find $v$ in terms of $t$.
[6]
\hfill \mbox{\textit{Edexcel M4 Q1 [6]}}