| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 12 |
| 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 mechanics question on non-constant acceleration requiring routine techniques: factorizing a quadratic to find when v=0, differentiating to find acceleration, integrating to find displacement, and comparing positions. All steps are algorithmic with no novel insight required, making it slightly easier than average. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration |
\begin{enumerate}
\item At time $t = 0$ a particle $P$ leaves the origin $O$ and moves along the $x$-axis. At time $t$ seconds, the velocity of $P$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the positive $x$ direction, where
\end{enumerate}
$$v = 3 t ^ { 2 } - 16 t + 21$$
The particle is instantaneously at rest when $t = t _ { 1 }$ and when $t = t _ { 2 } \left( t _ { 1 } < t _ { 2 } \right)$.\\
(a) Find the value of $t _ { 1 }$ and the value of $t _ { 2 }$.\\
(b) Find the magnitude of the acceleration of $P$ at the instant when $t = t _ { 1 }$.\\
(c) Find the distance travelled by $P$ in the interval $t _ { 1 } \leqslant t \leqslant t _ { 2 }$.\\
(d) Show that $P$ does not return to $O$.\\
\hfill \mbox{\textit{Edexcel M2 2017 Q4 [12]}}