| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Displacement-time graph interpretation or sketching |
| Difficulty | Moderate -0.8 This is a straightforward displacement-time graph question requiring basic interpretation skills. Part (a) uses gradient of a straight line, part (b) applies a standard SUVAT equation with constant acceleration, and part (c) calculates average speed from total distance and time. All parts involve routine calculations with no problem-solving insight required, making it easier than average but not trivial due to the multi-part nature. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time |
| Answer | Marks |
|---|---|
| \(\text{Speed} = 20 \text{ ms}^{-1}\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(20 = 0 + a \times 5\) | M1 | Use of \(v = u + at\) OE |
| \(a = 4 \text{ ms}^{-2}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\dfrac{50 + 100 + 50 + 200}{20}\) | M1 | Use of \(\dfrac{\text{total distance}}{\text{total time}}\) OE |
| \(\text{Average speed} = 20 \text{ ms}^{-1}\) | A1 |
## Question 3:
### Part (a):
$\text{Speed} = 20 \text{ ms}^{-1}$ | B1 |
### Part (b):
$20 = 0 + a \times 5$ | M1 | Use of $v = u + at$ OE
$a = 4 \text{ ms}^{-2}$ | A1 |
### Part (c):
$\dfrac{50 + 100 + 50 + 200}{20}$ | M1 | Use of $\dfrac{\text{total distance}}{\text{total time}}$ OE
$\text{Average speed} = 20 \text{ ms}^{-1}$ | A1 |
---3\\
\includegraphics[max width=\textwidth, alt={}, center]{4e555003-16f1-4453-ab25-c50929d4b5b3-04_824_1636_264_258}
The displacement of a particle moving in a straight line is $s$ metres at time $t$ seconds after leaving a fixed point $O$. The particle starts from rest and passes through points $P , Q$ and $R$, at times $t = 5 , t = 10$ and $t = 15$ respectively, and returns to $O$ at time $t = 20$. The distances $O P , O Q$ and $O R$ are 50 m , 150 m and 200 m respectively.
The diagram shows a displacement-time graph which models the motion of the particle from $t = 0$ to $t = 20$. The graph consists of two curved segments $A B$ and $C D$ and two straight line segments $B C$ and $D E$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of the particle between $t = 5$ and $t = 10$.
\item Find the acceleration of the particle between $t = 0$ and $t = 5$, given that it is constant.
\item Find the average speed of the particle during its motion.\\
\includegraphics[max width=\textwidth, alt={}, center]{4e555003-16f1-4453-ab25-c50929d4b5b3-06_483_880_258_630}
The diagram shows a block of mass 10 kg suspended below a horizontal ceiling by two strings $A C$ and $B C$, of lengths 0.8 m and 0.6 m respectively, attached to fixed points on the ceiling. Angle $A C B = 90 ^ { \circ }$. There is a horizontal force of magnitude $F \mathrm {~N}$ acting on the block. The block is in equilibrium.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2022 Q3 [5]}}