| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2012 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Acceleration as function of displacement (v dv/dx method) |
| Difficulty | Standard +0.3 This is a standard M3 variable acceleration question requiring integration of an exponential velocity function and use of the chain rule for acceleration. Part (a) needs v(dv/dx) = a, and part (b) requires integrating v = dx/dt with given initial conditions. While it involves exponential functions and careful algebraic manipulation, the techniques are routine for M3 students and the question follows a familiar template, making it slightly easier than average overall. |
| Spec | 1.08a Fundamental theorem of calculus: integration as reverse of differentiation3.02f Non-uniform acceleration: using differentiation and integration |
A particle $P$ is moving along the positive $x$-axis. At time $t = 0$, $P$ is at the origin $O$. At time $t$ seconds, $P$ is $x$ metres from $O$ and has velocity $v = 2e^{-t}$ m s$^{-1}$ in the direction of $x$ increasing.
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of $P$ in terms of $x$. [3]
\item Find $x$ in terms of $t$. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2012 Q1 [9]}}