| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Variable acceleration with initial conditions |
| Difficulty | Standard +0.3 This is a standard M2 variable acceleration question requiring integration of acceleration to find velocity, then solving v=0 for rest points, and integrating velocity to find displacement. While it involves multiple steps (11 marks total), each step follows routine procedures with no novel insight required. Slightly above average difficulty due to the multi-step nature and need to find two rest points then calculate distance between them. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration |
A particle $P$ moves on the $x$-axis. The acceleration of $P$ at time $t$ seconds is $(4t - 8)$ m s$^{-2}$, measured in the direction of $x$ increasing. The velocity of $P$ at time $t$ seconds is $v$ m s$^{-1}$. Given that $v = 6$ when $t = 0$, find
\begin{enumerate}[label=(\alph*)]
\item $v$ in terms of $t$,
[4]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the distance between the two points where $P$ is instantaneously at rest.
[7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q5 [11]}}