Standard +0.8 This M3 variable force question requires setting up and integrating F=ma with a position-dependent force, then applying energy/work principles to find a specific position. While the integration of 5/(x+1) is straightforward, students must correctly formulate the work-energy relationship and solve the resulting logarithmic equation. The multi-step nature and need to connect force, work, and kinematics makes this moderately challenging but still within standard M3 scope.
A particle \(P\) of mass 0.2 kg moves away from the origin along the positive \(x\)-axis. It moves under the action of a force directed away from the origin \(O\), of magnitude \(\frac{5}{x+1}\) N, where \(OP = x\) metres. Given that the speed of \(P\) is 5 m s\(^{-1}\) when \(x = 0\), find the value of \(x\), to 3 significant figures, when the speed of \(P\) is 15 m s\(^{-1}\).
[8]
A particle $P$ of mass 0.2 kg moves away from the origin along the positive $x$-axis. It moves under the action of a force directed away from the origin $O$, of magnitude $\frac{5}{x+1}$ N, where $OP = x$ metres. Given that the speed of $P$ is 5 m s$^{-1}$ when $x = 0$, find the value of $x$, to 3 significant figures, when the speed of $P$ is 15 m s$^{-1}$.
[8]
\hfill \mbox{\textit{Edexcel M3 2002 Q1 [8]}}