| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Sketching velocity-time graphs |
| Difficulty | Easy -1.2 This is a straightforward kinematics question involving reading values from a piecewise linear velocity-time graph and applying basic formulas: acceleration = gradient, distance = area under graph. All calculations are routine with no problem-solving insight required, making it easier than average. |
| Spec | 3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Acceleration is 0.02 ms⁻² | A1 | 3 |
| Acceleration is −0.21 ms⁻² | A1 | |
| M1 | For using the gradient property for acceleration or \(v = u + at\) | |
| (ii) \(\frac{1}{2}(1.5 + 2.1) \times 30 + \frac{1}{2} \times 2.1 \times 10 - \frac{1}{2} \times 2.2 \times 20\) | M1 | For using the area property for displacement |
| Distance AB is 42.5 m | A1 | 2 |
| (iii) Total distance walked is 86.5 m | B1ft | 1 |
(i) Acceleration is 0.02 ms⁻² | A1 | 3
Acceleration is −0.21 ms⁻² | A1 |
| M1 | For using the gradient property for acceleration or $v = u + at$
(ii) $\frac{1}{2}(1.5 + 2.1) \times 30 + \frac{1}{2} \times 2.1 \times 10 - \frac{1}{2} \times 2.2 \times 20$ | M1 | For using the area property for displacement
Distance AB is 42.5 m | A1 | 2
(iii) Total distance walked is 86.5 m | B1ft | 1 | It error in '64.5' or '22.0' or both1\\
\includegraphics[max width=\textwidth, alt={}, center]{155bc571-80e4-4c93-859f-bb150a109211-2_675_1380_255_379}
A woman walks in a straight line. The woman's velocity $t$ seconds after passing through a fixed point $A$ on the line is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The graph of $v$ against $t$ consists of 4 straight line segments (see diagram). The woman is at the point $B$ when $t = 60$. Find\\
(i) the woman's acceleration for $0 < t < 30$ and for $30 < t < 40$,\\
(ii) the distance $A B$,\\
(iii) the total distance walked by the woman.
\hfill \mbox{\textit{CAIE M1 2011 Q1 [6]}}