| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2006 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Velocity from acceleration by integration |
| Difficulty | Moderate -0.3 This is a straightforward M3 variable acceleration question requiring two standard integrations with given initial conditions. While it involves trigonometric functions, the steps are routine: integrate acceleration to find velocity using v=4 at t=0, then integrate velocity to find displacement. The calculation is direct with no conceptual challenges or problem-solving insight required, making it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration |
2. A particle $P$ moves along the $x$-axis. At time $t$ seconds the velocity of $P$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and its acceleration is $2 \sin \frac { 1 } { 2 } t \mathrm {~m} \mathrm {~s} ^ { - 2 }$, both measured in the direction of $O x$. Given that $v = 4$ when $t = 0$,
\begin{enumerate}[label=(\alph*)]
\item find $v$ in terms of $t$,
\item calculate the distance travelled by $P$ between the times $t = 0$ and $t = \frac { \pi } { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2006 Q2 [8]}}