| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Total distance with direction changes |
| Difficulty | Moderate -0.3 This is a standard M2 variable acceleration question requiring integration of acceleration to find velocity, then solving for when v=0, and finally integrating velocity for distance with attention to direction changes. While it involves multiple steps and careful handling of the 'total distance' aspect, the techniques are routine for M2 students with no novel problem-solving required. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration3.02g Two-dimensional variable acceleration |
3. A particle $P$ moves along the $x$-axis. At time $t = 0 , P$ passes through the origin with speed $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the positive $x$ direction. The acceleration of $P$ at time $t$ seconds, where $t \geqslant 0$, is $( 4 t - 8 ) \mathrm { m } \mathrm { s } ^ { - 2 }$ in the positive $x$ direction.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Show that $P$ is instantaneously at rest when $t = 1$
\item Find the other value of $t$ for which $P$ is instantaneously at rest.
\end{enumerate}\item Find the total distance travelled by $P$ in the interval $1 \leqslant t \leqslant 4$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2017 Q3 [9]}}