| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2004 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Displacement from velocity by integration |
| Difficulty | Moderate -0.3 This is a straightforward M3 variable acceleration question requiring two integrations with given initial conditions. The exponential function integrates cleanly, and finding instantaneous rest is a standard technique. While it requires calculus beyond C1-C2, it's a routine textbook exercise for M3 students with no novel problem-solving required. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration3.02g Two-dimensional variable acceleration |
2. A particle $P$ moves along the $x$-axis. At time $t$ seconds its acceleration is $\left( - 4 \mathrm { e } ^ { - 2 t } \right) \mathrm { m } \mathrm { s } ^ { - 2 }$ in the direction of $x$ increasing. When $t = 0 , P$ is at the origin $O$ and is moving with speed $1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the direction of $x$ increasing.
\begin{enumerate}[label=(\alph*)]
\item Find an expression for the velocity of $P$ at time $t$.
\item Find the distance of $P$ from $O$ when $P$ comes to instantaneous rest.\\
(6)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2004 Q2 [9]}}