Moderate -0.3 This is a straightforward M2 kinematics question requiring integration of a given velocity function and finding when v=0. The steps are routine: solve 6t-2t²=0 for the non-zero root (t=3), then integrate v to find displacement x=3t²-⅔t³ and evaluate at t=3. While it requires multiple steps (5 marks), all techniques are standard M2 procedures with no conceptual challenges or problem-solving insight needed.
A particle \(P\) moves on the \(x\)-axis. At time \(t\) seconds the velocity of \(P\) is \(v\) m s\(^{-1}\) in the direction of \(x\) increasing, where \(v = 6t - 2t^2\). When \(t = 0\), \(P\) is at the origin \(O\). Find the distance of \(P\) from \(O\) when \(P\) comes to instantaneous rest after leaving \(O\).
[5]
A particle $P$ moves on the $x$-axis. At time $t$ seconds the velocity of $P$ is $v$ m s$^{-1}$ in the direction of $x$ increasing, where $v = 6t - 2t^2$. When $t = 0$, $P$ is at the origin $O$. Find the distance of $P$ from $O$ when $P$ comes to instantaneous rest after leaving $O$.
[5]
\hfill \mbox{\textit{Edexcel M2 2003 Q1 [5]}}