| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Total distance with direction changes |
| Difficulty | Standard +0.3 This is a standard M2 variable acceleration question requiring differentiation for acceleration, integration for displacement with attention to direction changes, and analysis of when displacement equals zero. While it requires careful handling of sign changes and multiple techniques, these are routine M2 skills with no novel insight needed—slightly above average due to the multi-part nature and need to track direction changes carefully. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration |
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
$$v = (t - 2)(3t - 10), \quad t \geq 0$$
When $t = 0$, $P$ is at the origin $O$.
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of $P$ when $t = 3$ [3]
\item Find the total distance travelled by $P$ in the first 3 seconds of its motion. [6]
\item Show that $P$ never returns to $O$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2014 Q2 [11]}}