| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2024 |
| Session | March |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Displacement-time graph interpretation or sketching |
| Difficulty | Easy -1.3 This is a straightforward travel graphs question requiring basic interpretation of a displacement-time graph. Part (a) involves simple calculation using distance/time (gradient of a line segment), and part (b) requires converting gradients to a velocity-time sketch—both are routine skills with no problem-solving or conceptual challenges beyond standard M1 content. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area |
| Answer | Marks | Guidance |
|---|---|---|
| 1(a) | Total distance travelled = 50+210 =70 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 20 | B1FT | Oe. |
| Answer | Marks | Guidance |
|---|---|---|
| 1(b) | Velocity 5 ms–1 for 0 t 10 | B1 |
| B1 | Stepped diagram with four horizontal lines segments. |
| Answer | Marks |
|---|---|
| B1FT | All correct. |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 1:
--- 1(a) ---
1(a) | Total distance travelled = 50+210 =70 | B1 | Any explicit expression for the distance,
x−50
e.g. =2 →x=2(20−10)+50.
20−10
70
Velocity =− = −3.5m s–1
20 | B1FT | Oe.
Ft their distance 50.
Must be negative.
Do not ISW if (e.g.) velocity = 3.5.
Do allow “3.5ms–1, directed towards O.”
2
--- 1(b) ---
1(b) | Velocity 5 ms–1 for 0 t 10 | B1 | May be seen on diagram.
B1 | Stepped diagram with four horizontal lines segments.
Ignore vertical line segments.
B1FT | All correct.
10, 20, 40 and 60 indicated on the t-axis.
Their 5, 2 and their –3.5 (allow –3 and –4 is
acceptable too with line segment halfway between
them) indicated on the v-axis, corresponding to the
position of the horizontal line segments.
FT their –3.5 ms–1 and/or FT their 5 ms–1.
If their answer to (a) is positive, allow use of
negative their answer for this mark.
3
Question | Answer | Marks | Guidance\includegraphics{figure_1}
The displacement of a particle at time $t$ s after leaving a fixed point $O$ is $s$ m. The diagram shows a displacement-time graph which models the motion of the particle. The graph consists of 4 straight line segments. The particle travels 50 m in the first 10 s, then travels at $2$ m s$^{-1}$ for a period of 10 s. The particle then comes to rest for a period of 20 s, before returning to its starting point when $t = 60$.
\begin{enumerate}[label=(\alph*)]
\item Find the velocity of the particle during the last 20 s of its motion. [2]
\item Sketch a velocity-time graph for the motion of the particle from $t = 0$ to $t = 60$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2024 Q1 [5]}}