| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Force depends on time t |
| Difficulty | Standard +0.3 This is a straightforward M3 variable force question requiring integration of F=ma to find velocity, then integration again to find displacement. The force function is simple (linear in t), the initial conditions are clearly stated, and part (b) only requires finding when v=6 and substituting into the position equation. Standard textbook exercise with no conceptual challenges beyond applying Newton's second law with calculus. |
| Spec | 6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.06a Variable force: dv/dt or v*dv/dx methods |
2. A particle $P$ of mass 0.5 kg is moving along the positive $x$-axis in the positive $x$-direction. The only force on $P$ is a force of magnitude $\left( 2 t + \frac { 1 } { 2 } \right) \mathrm { N }$ acting in the direction of $x$ increasing, where $t$ seconds is the time after $P$ leaves the origin $O$. When $t = 0$, $P$ is at rest at $O$.
\begin{enumerate}[label=(\alph*)]
\item Find an expression, in terms of $t$, for the velocity of $P$ at time $t$ seconds.
The particle passes through the point $A$ with speed $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\item Find the distance $O A$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2013 Q2 [9]}}