Standard +0.3 This is a standard M4 variable force/resistance problem requiring separation of variables and integration. The setup is straightforward (F=ma with resistance 2v), and the method is routine for this module. It's slightly above average difficulty due to requiring calculus and careful algebraic manipulation, but follows a well-practiced template with no conceptual surprises.
A particle \(P\) of mass 3 kg moves in a straight line on a smooth horizontal plane. When the speed of \(P\) is \(v\) m s\(^{-1}\), the resultant force acting on \(P\) is a resistance to motion of magnitude \(2v\) N. Find the distance moved by \(P\) while slowing down from 5 m s\(^{-1}\) to 2 m s\(^{-1}\).
[5]
A particle $P$ of mass 3 kg moves in a straight line on a smooth horizontal plane. When the speed of $P$ is $v$ m s$^{-1}$, the resultant force acting on $P$ is a resistance to motion of magnitude $2v$ N. Find the distance moved by $P$ while slowing down from 5 m s$^{-1}$ to 2 m s$^{-1}$.
[5]
\hfill \mbox{\textit{Edexcel M4 2004 Q1 [5]}}