| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | November |
| 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 acceleration from gradient, finding velocity from given conditions, and using area under graph for displacement. All techniques are standard GCSE/AS-level mechanics with clear step-by-step structure and no novel problem-solving 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 |
|---|---|---|
| 3(i) | Acceleration = –1 m s–2 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(ii) | [V/4 = 1 or (V + 2)/6 = 1] | M1 |
| Answer | Marks |
|---|---|
| V = 4 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(iii) | [Distance = Area = ½ (6 + 2) × 2 = 8] | M1 |
| Distance AB = 3 × 8 = 24 m | A1 | |
| [½ × (T – 6) × 4 = 24] | M1 | Attempt to find the distance travelled from t = 6 to t = T and set up an |
| Answer | Marks |
|---|---|
| T = 18 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(i) ---
3(i) | Acceleration = –1 m s–2 | B1 | Allow deceleration = 1 m s–2
1
--- 3(ii) ---
3(ii) | [V/4 = 1 or (V + 2)/6 = 1] | M1 | Use of gradient of line between t = 4 and t = 10 or use of similar triangles
to find V
V = 4 | A1
2
--- 3(iii) ---
3(iii) | [Distance = Area = ½ (6 + 2) × 2 = 8] | M1 | Attempt distance travelled in first 6 seconds
Distance AB = 3 × 8 = 24 m | A1
[½ × (T – 6) × 4 = 24] | M1 | Attempt to find the distance travelled from t = 6 to t = T and set up an
equation for T
T = 18 | A1
4
Question | Answer | Marks | Guidance\includegraphics{figure_3}
The velocity of a particle moving in a straight line is $v$ m s$^{-1}$ at time $t$ seconds. The diagram shows a velocity-time graph which models the motion of the particle from $t = 0$ to $t = T$. The graph consists of four straight line segments. The particle reaches its maximum velocity $V$ m s$^{-1}$ at $t = 10$.
\begin{enumerate}[label=(\roman*)]
\item Find the acceleration of the particle during the first $2$ seconds. [1]
\item Find the value of $V$. [2]
\end{enumerate}
At $t = 6$, the particle is instantaneously at rest at the point $A$. At $t = T$, the particle comes to rest at the point $B$. At $t = 0$ the particle starts from rest at a point one third of the way from $A$ to $B$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the distance $AB$ and hence find the value of $T$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2018 Q3 [7]}}