| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Distance from velocity-time graph |
| Difficulty | Moderate -0.8 This is a straightforward velocity-time graph interpretation question requiring students to find areas under the graph (for distances) and sketch a displacement-time graph. The concepts are basic kinematics with clear visual cues, requiring only area calculations (triangles/rectangles) and understanding that displacement is the integral of velocity. No complex problem-solving or novel insight needed—standard M1 material that's easier than average A-level questions. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Distance \(AC\) is 70 m | B1 | |
| \(7\times10 - 4\times15\) | M1 | For using \( |
| Distance \(AB\) is 10 m | A1 (×3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Graph: 3 connected straight line segments | M1 | Graph consists of 3 connected straight line segments with, in order, positive, zero and negative slopes; \(x(t)\) is single valued and graph contains the origin |
| 1st line segment steeper than 3rd | A1 | 1st line segment appears steeper than 3rd and 3rd line segment does not terminate on \(t\)-axis |
| Values of \(t\) (10, 15 and 30) and \(x\) (70, 70, 10) shown | A1 ft (×3) | Values of \(t\) (10, 15 and 30) and \(x\) (70, 70, 10) shown, or can be read without ambiguity from scales; SR (max 1 out of 3): for first 2 segments correct B1 |
# Question 3:
## Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Distance $AC$ is 70 m | B1 | |
| $7\times10 - 4\times15$ | M1 | For using $|AB| = |AC| - |BC|$ |
| Distance $AB$ is 10 m | A1 (×3) | |
## Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Graph: 3 connected straight line segments | M1 | Graph consists of 3 connected straight line segments with, in order, positive, zero and negative slopes; $x(t)$ is single valued and graph contains the origin |
| 1st line segment steeper than 3rd | A1 | 1st line segment appears steeper than 3rd and 3rd line segment does not terminate on $t$-axis |
| Values of $t$ (10, 15 and 30) and $x$ (70, 70, 10) shown | A1 ft (×3) | Values of $t$ (10, 15 and 30) and $x$ (70, 70, 10) shown, or can be read without ambiguity from scales; SR (max 1 out of 3): for first 2 segments correct B1 |
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\includegraphics[max width=\textwidth, alt={}, center]{e060fc3b-ae93-46b5-b476-dcecb14d6d06-3_727_899_267_625}
A boy runs from a point $A$ to a point $C$. He pauses at $C$ and then walks back towards $A$ until reaching the point $B$, where he stops. The diagram shows the graph of $v$ against $t$, where $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is the boy's velocity at time $t$ seconds after leaving $A$. The boy runs and walks in the same straight line throughout.\\
(i) Find the distances $A C$ and $A B$.\\
(ii) Sketch the graph of $x$ against $t$, where $x$ metres is the boy's displacement from $A$. Show clearly the values of $t$ and $x$ when the boy arrives at $C$, when he leaves $C$, and when he arrives at $B$. [3]
\hfill \mbox{\textit{CAIE M1 2004 Q3 [6]}}