| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Vertical projection: speed of projection |
| Difficulty | Moderate -0.8 This is a straightforward SUVAT question requiring standard application of kinematic equations. Part (a) uses v²=u²+2as with v=0 at maximum height to find initial speed. Part (b) requires finding times when speed equals 10 m/s on ascent and descent, then calculating the difference—routine mechanics with no conceptual challenges beyond basic SUVAT manipulation. |
| Spec | 3.02h Motion under gravity: vector form6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0 = u^2 - 2g \times 45\) | M1 | For use of \(v^2 = u^2 + 2as\); OE complete method that would lead to finding \(u\) |
| Speed \(= 30 \text{ ms}^{-1}\) | A1 | |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(10 = 30 - gt\) leading to \(t = 2\) | M1 | For use of \(v = u + at\) to find time to \(10 \text{ ms}^{-1}\), or use of '*suvat*' to find time for one stage of motion |
| \(2 \times 2 \text{ s}\) | M1 | \(2 \times\) time to \(10 \text{ ms}^{-1}\) OE |
| Total time \(= 4 \text{ s}\) | A1 | |
| Total: 3 |
## Question 2:
**Part (a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0 = u^2 - 2g \times 45$ | M1 | For use of $v^2 = u^2 + 2as$; OE complete method that would lead to finding $u$ |
| Speed $= 30 \text{ ms}^{-1}$ | A1 | |
| | **Total: 2** | |
**Part (b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $10 = 30 - gt$ leading to $t = 2$ | M1 | For use of $v = u + at$ to find time to $10 \text{ ms}^{-1}$, or use of '*suvat*' to find time for one stage of motion |
| $2 \times 2 \text{ s}$ | M1 | $2 \times$ time to $10 \text{ ms}^{-1}$ OE |
| Total time $= 4 \text{ s}$ | A1 | |
| | **Total: 3** | |2 A particle $P$ is projected vertically upwards from horizontal ground. $P$ reaches a maximum height of 45 m . After reaching the ground, $P$ comes to rest without rebounding.
\begin{enumerate}[label=(\alph*)]
\item Find the speed at which $P$ was projected.
\item Find the total time for which the speed of $P$ is at least $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2022 Q2 [5]}}