| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2019 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Given acceleration function find velocity |
| Difficulty | Standard +0.8 This M3 question requires recognizing that acceleration as a function of displacement (not time) necessitates using v dv/dx = a, then integrating and applying initial conditions to find where v=0. While the integration itself is straightforward, the conceptual step of choosing the correct kinematic relationship and setting up the problem correctly elevates this above routine calculus questions. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y)4.10f Simple harmonic motion: x'' = -omega^2 x6.06a Variable force: dv/dt or v*dv/dx methods |
\begin{enumerate}
\item A particle $P$ moves on the $x$-axis. At time $t$ seconds, $t \geqslant 0$, the displacement of $P$ from the origin $O$ is $x$ metres and the acceleration of $P$ is $\left( \frac { 7 } { 2 } - 2 x \right) \mathrm { m } \mathrm { s } ^ { - 2 }$, measured in the positive $x$ direction. At time $t = 0 , P$ passes through $O$ moving with speed $3 \mathrm {~ms} ^ { - 1 }$ in the positive $x$ direction. Find the distance of $P$ from $O$ when $P$ first comes to instantaneous rest.\\
(6)\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2019 Q1 [6]}}