| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2002 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Piecewise motion functions |
| Difficulty | Standard +0.3 This is a straightforward M2 variable acceleration question requiring integration of piecewise acceleration functions to find velocity. Part (a) involves a single polynomial integration with given initial conditions. Part (b) requires using the velocity from part (a) as the initial condition for the second interval and integrating a simple power function. The techniques are standard and well-practiced in M2, with no conceptual challenges beyond careful bookkeeping of the piecewise definition. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums3.02f Non-uniform acceleration: using differentiation and integration |
A particle $P$ moves in a straight line so that, at time $t$ seconds, its acceleration $a$ m s$^{-2}$ is given by
$$a = \begin{cases}
4t - t^2, & 0 \leq t \leq 3, \\
\frac{27}{t^2}, & t > 3.
\end{cases}$$
At $t = 0$, $P$ is at rest. Find the speed of $P$ when
\begin{enumerate}[label=(\alph*)]
\item $t = 3$, [3]
\item $t = 6$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2002 Q2 [8]}}