| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2019 |
| Session | March |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with velocity-time graph given |
| Difficulty | Moderate -0.8 This is a straightforward velocity-time graph question requiring basic kinematics: calculating distance as area under the graph (trapezium rule) and using displacement constraints to find an unknown velocity. The multi-step nature and 7 total marks elevate it slightly above trivial, but it involves only standard techniques with no problem-solving insight required. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| 5(i) | Velocity at t = 3 is 3 × 3 = 9 | B1 |
| [½ × 3 × 9 + ½ (9 + 7) × 2 + ½ × 3 × 7] | M1 | Attempt distance travelled in the first 8 seconds using |
| Answer | Marks |
|---|---|
| Distance = 40 m | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 5(ii) | [32 = 40 + area of triangle] | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| (–)8 | A1 | |
| [Distance = ½ × 8 × V = (–)8] | M1 | Set up an equation for the area of triangle involving V |
| Answer | Marks |
|---|---|
| V = –2 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 5:
--- 5(i) ---
5(i) | Velocity at t = 3 is 3 × 3 = 9 | B1
[½ × 3 × 9 + ½ (9 + 7) × 2 + ½ × 3 × 7] | M1 | Attempt distance travelled in the first 8 seconds using
Distance = area under graph.
Distance = 40 m | A1
3
Question | Answer | Marks | Guidance
--- 5(ii) ---
5(ii) | [32 = 40 + area of triangle] | M1 | Use given displacement to set up equation for area of triangle
or attempt to find distance or displacement from t = 8 to t =
16
Area of triangle or displacement/distance =
(–)8 | A1
[Distance = ½ × 8 × V = (–)8] | M1 | Set up an equation for the area of triangle involving V
or use suvat equations to set up an equation involving V
V = –2 | A1
4
Question | Answer | Marks | Guidance\includegraphics{figure_5}
The velocity of a particle moving in a straight line is $v$ m s$^{-1}$ at time $t$ seconds after leaving a fixed point $O$. The diagram shows a velocity-time graph which models the motion of the particle from $t = 0$ to $t = 16$. The graph consists of five straight line segments. The acceleration of the particle from $t = 0$ to $t = 3$ is $\frac{7}{3}$ m s$^{-2}$. The velocity of the particle at $t = 5$ is $7$ m s$^{-1}$ and it comes to instantaneous rest at $t = 8$. The particle then comes to rest again at $t = 16$. The minimum velocity of the particle is $V$ m s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\item Find the distance travelled by the particle in the first $8$ s of its motion. [3]
\item Given that when the particle comes to rest at $t = 16$ its displacement from $O$ is $32$ m, find the value of $V$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2019 Q5 [7]}}