| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2020 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Particle instantaneously at rest |
| Difficulty | Moderate -0.3 This is a straightforward mechanics question requiring standard differentiation to find acceleration and integration to find position. Part (a) is routine differentiation of polynomials. Part (b) requires finding when v=0 (solving two quadratics), then integrating velocity to get position and calculating distance—all standard M2 techniques with no novel problem-solving required. Slightly easier than average due to the mechanical nature of the calculations. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration3.02g Two-dimensional variable acceleration |
5. At time $t$ seconds ( $t \geqslant 0$ ), a particle $P$ has velocity $\mathbf { v m ~ s } ^ { - 1 }$, where
$$\mathbf { v } = \left( 3 t ^ { 2 } - 9 t + 6 \right) \mathbf { i } + \left( t ^ { 2 } + t - 6 \right) \mathbf { j }$$
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of $P$ when $t = 3$
When $t = 0 , P$ is at the fixed point $O$.\\
The particle comes to instantaneous rest at the point $A$.
\item Find the distance $O A$.
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\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2020 Q5 [10]}}