| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Forces and Newton's second law with kinematics |
| Difficulty | Standard +0.3 This is a standard M1 momentum and impulse question requiring conservation of momentum, impulse-momentum theorem, and Newton's third law. While it involves multiple parts and algebraic manipulation with masses and velocities, the techniques are routine textbook applications with no novel problem-solving insight required. The 12 marks reflect length rather than conceptual difficulty, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Momentum: \(18u - 16v = -18(u/2) + 16v\) | M1 A1 A1 | |
| \(2u = -9u + 16v\) → \(11u = 16v\) → \(v = \frac{11u}{16}\) | M1 A1 | |
| (b) Velocity of Q was negative, now positive, so direction reversed | B1 | |
| (c) Impulse \(= 16000(u + \frac{11u}{16}) = 27000u\) Ns | M1 A1 B1 | |
| (d) \(108000u = 27000u\) → \(t = 0.25\) s | M1 A1 A1 | Total: 12 marks |
**(a)** Momentum: $18u - 16v = -18(u/2) + 16v$ | M1 A1 A1 |
$2u = -9u + 16v$ → $11u = 16v$ → $v = \frac{11u}{16}$ | M1 A1 |
**(b)** Velocity of Q was negative, now positive, so direction reversed | B1 |
**(c)** Impulse $= 16000(u + \frac{11u}{16}) = 27000u$ Ns | M1 A1 B1 |
**(d)** $108000u = 27000u$ → $t = 0.25$ s | M1 A1 A1 | **Total: 12 marks**Two trucks $P$ and $Q$, of masses 18 000 kg and 16 000 kg respectively, collide while moving towards each other in a straight line. Immediately before the collision, both trucks are travelling at the same speed, $u$ ms$^{-1}$. Immediately after the collision, $P$ is moving at half its original speed, its direction of motion having been reversed.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $u$, the speed of $Q$ immediately after the collision. \hfill [5 marks]
\item State, with a reason, whether the direction of $Q$'s motion has been reversed. \hfill [1 mark]
\item Find, in terms of $u$, the magnitude of the impulse exerted by $P$ on $Q$ in the collision, stating the units of your answer. \hfill [3 marks]
\end{enumerate}
The force exerted by each truck on the other in the impact has magnitude $108000u$ N.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the time for which the trucks are in contact. \hfill [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [12]}}