| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2019 |
| 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 -0.8 This is a straightforward velocity-time graph question requiring basic kinematics: part (i) uses acceleration = change in velocity / time to find V, and part (ii) uses area under graph = distance to find U. Both parts involve simple algebraic manipulation with no conceptual challenges beyond standard GCSE/AS-level mechanics. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| 2(i) | ( ) |
| Answer | Marks | Guidance |
|---|---|---|
| 35−30 | M1 | Use gradient of graph or constant acceleration formulae to set up |
| Answer | Marks |
|---|---|
| V=8 | A1 |
| Answer | Marks |
|---|---|
| 2(ii) | 25×8+5×10+15×6+ 1 ×( U +8 )×5=375 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | M1 | Attempt to find total distance travelled by the tractor in 50s to |
| Answer | Marks |
|---|---|
| A1FT | Correct equation FT on their V from (i) |
| U=6 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Mark |
Question 2:
--- 2(i) ---
2(i) | ( )
12−V
=0.8 or 12 = V + 0.8 × 5
( )
35−30 | M1 | Use gradient of graph or constant acceleration formulae to set up
an equation in V
V=8 | A1
2
--- 2(ii) ---
2(ii) | 25×8+5×10+15×6+ 1 ×( U +8 )×5=375
2 | M1 | Attempt to find total distance travelled by the tractor in 50s to
set up an equation for U using EITHER areas
OR suvat equations OR a combination of areas and suvat
In either case total distance must be attempted
A1FT | Correct equation FT on their V from (i)
U=6 | A1
3
Question | Answer | Mark | Guidance\includegraphics{figure_2}
The diagram shows a velocity-time graph which models the motion of a tractor. The graph consists of four straight line segments. The tractor passes a point $O$ at time $t = 0$ with speed $U$ m s$^{-1}$. The tractor accelerates to a speed of $V$ m s$^{-1}$ over a period of 5 s, and then travels at this speed for a further 25 s. The tractor then accelerates to a speed of 12 m s$^{-1}$ over a period of 5 s. The tractor then decelerates to rest over a period of 15 s.
\begin{enumerate}[label=(\roman*)]
\item Given that the acceleration of the tractor between $t = 30$ and $t = 35$ is 0.8 m s$^{-2}$, find the value of $V$. [2]
\item Given also that the total distance covered by the tractor in the 50 seconds of motion is 375 m, find the value of $U$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2019 Q2 [5]}}