| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Vertical motion: velocity-time graph |
| Difficulty | Standard +0.3 Part (i) requires calculating area under a velocity-time graph (trapezium rule), which is straightforward SUVAT application. Part (ii) involves applying Newton's second law with given deceleration from the graph and weight, requiring F = ma with net force calculation. Both are standard M1 techniques with clear data provided, slightly above average due to multi-stage setup and forces calculation. |
| Spec | 3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae3.03d Newton's second law: 2D vectors |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \([\frac{1}{2}5 \times 50 + \frac{1}{2}7(8 + 50) + 90 \times 8]\) | M1 | For using the area property for distance or \(s = \frac{1}{2}(u + v)t\) |
| Distance is 1048 m | A1 | [2] |
| (ii) | M1 | For use of the gradient property for acceleration (deceleration) |
| \(a = (8 - 50)(12 - 5)\) or \(d = (50 - 8)(12 - 5)\) | A1 | |
| M1 | For using Newton's second law (3 terms) | |
| \(850 - F = 85a\) (or \(-85d\)) | A1 | |
| Upward force is 1360 N | A1 | [5] |
**(i)** $[\frac{1}{2}5 \times 50 + \frac{1}{2}7(8 + 50) + 90 \times 8]$ | M1 | For using the area property for distance or $s = \frac{1}{2}(u + v)t$
Distance is 1048 m | A1 | [2] | AG
**(ii)** | M1 | For use of the gradient property for acceleration (deceleration)
$a = (8 - 50)(12 - 5)$ or $d = (50 - 8)(12 - 5)$ | A1 |
| M1 | For using Newton's second law (3 terms)
$850 - F = 85a$ (or $-85d$) | A1 |
Upward force is 1360 N | A1 | [5]3\\
\includegraphics[max width=\textwidth, alt={}, center]{d3bb6702-231d-42a0-830e-9f844dca78d7-2_748_1410_979_370}
The velocity-time graph shown models the motion of a parachutist falling vertically. There are four stages in the motion:
\begin{itemize}
\item falling freely with the parachute closed,
\item decelerating at a constant rate with the parachute open,
\item falling with constant speed with the parachute open,
\item coming to rest instantaneously on hitting the ground.\\
(i) Show that the total distance fallen is 1048 m .
\end{itemize}
The weight of the parachutist is 850 N .\\
(ii) Find the upward force on the parachutist due to the parachute, during the second stage.
\hfill \mbox{\textit{CAIE M1 2011 Q3 [7]}}