| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with velocity-time graph given |
| Difficulty | Moderate -0.5 This is a straightforward SUVAT and velocity-time graph question requiring basic kinematic equations and area calculations. Part (a) uses simple v=u+at, while part (b) involves calculating areas under the graph segments and solving a linear equation. The multi-stage setup adds slight complexity but follows standard M1 patterns with no novel problem-solving required. |
| Spec | 3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\left[2 = \frac{20}{T}\right] \rightarrow T = 10\) | B1 | |
| 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Distance before constant speed \(= \frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5\) or \(\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20-V)\times 5 + 5V\ [=150+2.5V]\) | B1 FT | May be implied if seen within total distance. FT on \(T\) value from 4(a) |
| Distance after constant speed \(= 27.5V + \frac{1}{2}\times 5V\ [=30V]\) | B1 | May be implied if seen within total distance |
| \(\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5 = \frac{1}{3}\left[\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5 + 27.5V + \frac{1}{2}\times 5V\right]\) | M1 | For attempting to use \(\frac{1}{2}\) or \(\frac{1}{3}\) correctly and for obtaining an equation for \(V\) which includes all parts of the journey, or \(\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5 = \frac{1}{2}\left[27.5V + \frac{1}{2}\times 5V\right]\) |
| \(V = 12\) | A1 | |
| 4 |
## Question 4:
**Part (a):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\left[2 = \frac{20}{T}\right] \rightarrow T = 10$ | B1 | |
| | **1** | |
**Part (b):**
| Answer | Mark | Guidance |
|--------|------|----------|
| Distance before constant speed $= \frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5$ or $\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20-V)\times 5 + 5V\ [=150+2.5V]$ | B1 FT | May be implied if seen within total distance. FT on $T$ value from **4(a)** |
| Distance after constant speed $= 27.5V + \frac{1}{2}\times 5V\ [=30V]$ | B1 | May be implied if seen within total distance |
| $\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5 = \frac{1}{3}\left[\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5 + 27.5V + \frac{1}{2}\times 5V\right]$ | M1 | For attempting to use $\frac{1}{2}$ or $\frac{1}{3}$ correctly and for obtaining an equation for $V$ which includes all parts of the journey, or $\frac{1}{2}\times 10\times 20 + \frac{1}{2}\times(20+V)\times 5 = \frac{1}{2}\left[27.5V + \frac{1}{2}\times 5V\right]$ |
| $V = 12$ | A1 | |
| | **4** | |
---4\\
\begin{tikzpicture}[>=latex]
% Axes
\draw[thick,->] (0,0) -- (10.5,0) node[right] {$t$\,(s)};
\draw[thick,->] (0,0) -- (0,5.5) node[above left] {$v$\,(m\,s$^{-1}$)};
% Origin label
\node[below left] at (0,0) {0};
% The velocity-time graph
\draw[thick] (0,0) -- (2,4) -- (3,2.4) -- (8,2.4) -- (9.5,0);
% Dashed lines for 20
\draw[dashed] (0,4) -- (2,4);
\draw[dashed] (2,4) -- (2,0);
% Dashed line for V
\draw[dashed] (0,2.4) -- (3,2.4);
% Axis labels
\node[left] at (0,4) {20};
\node[left] at (0,2.4) {$V$};
\node[below] at (2,0) {$T$};
\end{tikzpicture}
The diagram shows a velocity-time graph which models the motion of a car. The graph consists of four straight line segments. The car accelerates at a constant rate of $2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ from rest to a speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ over a period of $T \mathrm {~s}$. It then decelerates at a constant rate for 5 seconds before travelling at a constant speed of $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ for 27.5 s . The car then decelerates to rest at a constant rate over a period of 5 s .
\begin{enumerate}[label=(\alph*)]
\item Find $T$.
\item Given that the distance travelled up to the point at which the car begins to move with constant speed is one third of the total distance travelled, find $V$.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q4 [5]}}