Standard +0.8 This is a variable force problem requiring students to set up and solve a differential equation (F=ma with v dv/ds or dv/dt), then separate variables and integrate. While the setup is standard M2 content, the 7-mark allocation indicates multiple steps including correct force equation, separation of variables, integration, and applying initial conditions. It's moderately challenging but follows a well-practiced method for this topic.
A particle of mass \(m\) moves in a straight line. At time \(t\), its displacement from a fixed point on the line is \(s\) and its velocity is \(v\). The particle experiences a retarding force of magnitude \(mkv^2\), where \(k\) is a positive constant.
Find the relationship between \(v\) and \(t\). [7]
A particle of mass $m$ moves in a straight line. At time $t$, its displacement from a fixed point on the line is $s$ and its velocity is $v$. The particle experiences a retarding force of magnitude $mkv^2$, where $k$ is a positive constant.
Find the relationship between $v$ and $t$. [7]
\hfill \mbox{\textit{CAIE M2 2014 Q1 [7]}}