| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Finding constants from motion conditions |
| Difficulty | Standard +0.3 This is a straightforward mechanics problem requiring differentiation of a quadratic speed function and using three given conditions to find constants. The minimum condition gives dv/dt=0, providing a linear equation in p and q, while the two speed values give two more equations. Once constants are found, part (a) requires simple differentiation and substitution, and part (b) requires integration between t=2 and t=3. All steps are routine M2 techniques with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration |
\begin{enumerate}
\item A particle $P$ moves along a straight line. The speed of $P$ at time $t$ seconds ( $t \geqslant 0$ ) is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, where $v = \left( p t ^ { 2 } + q t + r \right)$ and $p , q$ and $r$ are constants. When $t = 2$ the speed of $P$ has its minimum value. When $t = 0 , v = 11$ and when $t = 2 , v = 3$
\end{enumerate}
Find\\
(a) the acceleration of $P$ when $t = 3$\\
(b) the distance travelled by $P$ in the third second of the motion.\\
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\hfill \mbox{\textit{Edexcel M2 2016 Q1 [13]}}