| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Total distance with direction changes |
| Difficulty | Moderate -0.8 This is a straightforward M2 kinematics question requiring only standard techniques: factorizing a quadratic to find when v=0, evaluating v at critical points and endpoints for maximum speed, and integrating |v| between rest points for distance. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial due to the multi-part nature and need for careful sign consideration. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown3.02a Kinematics language: position, displacement, velocity, acceleration3.02c Interpret kinematic graphs: gradient and area |
3. A particle $P$ moves on the $x$-axis. At time $t$ seconds the velocity of $P$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the direction of $x$ increasing, where
$$v = 2 t ^ { 2 } - 14 t + 20 , \quad t \geqslant 0$$
Find
\begin{enumerate}[label=(\alph*)]
\item the times when $P$ is instantaneously at rest,
\item the greatest speed of $P$ in the interval $0 \leqslant t \leqslant 4$
\item the total distance travelled by $P$ in the interval $0 \leqslant t \leqslant 4$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2013 Q3 [13]}}