Moderate -0.8 This is a straightforward mechanics question requiring two differentiations of given position vectors and then finding magnitude. It's routine calculus application with no problem-solving insight needed, making it easier than average, though the vector context adds slight complexity beyond pure differentiation.
At time \(t\) seconds, a particle \(P\) has position vector \(r\) metres relative to a fixed origin \(O\), where
$$r = (t^2 + 2t)\mathbf{i} + (t - 2t^2)\mathbf{j}.$$
Show that the acceleration of \(P\) is constant and find its magnitude.
[5]
At time $t$ seconds, a particle $P$ has position vector $r$ metres relative to a fixed origin $O$, where
$$r = (t^2 + 2t)\mathbf{i} + (t - 2t^2)\mathbf{j}.$$
Show that the acceleration of $P$ is constant and find its magnitude.
[5]
\hfill \mbox{\textit{Edexcel M2 Q1 [5]}}