Moderate -0.3 This is a straightforward differentiation exercise requiring students to find velocity (first derivative) and acceleration (second derivative) of a position vector, then calculate magnitude. While it involves vectors and two differentiations, it's a standard M2 technique with no problem-solving insight required—slightly easier than average due to its routine nature.
At time \(t\) seconds, a particle \(P\) has position vector \(r\) metres relative to a fixed origin \(O\), where
$$\mathbf{r} = (t^2 + 2t)\mathbf{i} + (t - 2t^2)\mathbf{j}.$$
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
$$\mathbf{r} = (t^2 + 2t)\mathbf{i} + (t - 2t^2)\mathbf{j}.$$
Show that the acceleration of $P$ is constant and find its magnitude.
[5]
\hfill \mbox{\textit{Edexcel M2 2001 Q1 [5]}}