| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Multi-phase journey: find unknown speed or time |
| Difficulty | Moderate -0.3 This is a standard SUVAT problem requiring students to connect three motion phases using given constraints. While it involves multiple stages and algebraic manipulation, the approach is methodical: use constant velocity section to find v, then apply standard SUVAT equations to find a and total time. The structure is typical for M1 with no novel insight required, making it slightly easier than average A-level difficulty. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Trapezium shape with gradient of right-hand side approximately 2 times left side | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Constant velocity \(= 500/25 = 20\ \text{ms}^{-1}\) | B1 | |
| \(20^2 = 0 + 2a \times 50\) | M1 | |
| \(a = 4\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Time to accelerate \(= 20/4 = 5\ \text{s}\) | B1 | |
| Deceleration time \(= 2.5\ \text{s}\) | B1 | |
| So total time \(= 5 + 25 + 2.5 = 32.5\ \text{s}\) | B1 |
## Question 4(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Trapezium shape with gradient of right-hand side approximately 2 times left side | B1 | |
## Question 4(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Constant velocity $= 500/25 = 20\ \text{ms}^{-1}$ | B1 | |
| $20^2 = 0 + 2a \times 50$ | M1 | |
| $a = 4$ | A1 | |
## Question 4(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| Time to accelerate $= 20/4 = 5\ \text{s}$ | B1 | |
| Deceleration time $= 2.5\ \text{s}$ | B1 | |
| So total time $= 5 + 25 + 2.5 = 32.5\ \text{s}$ | B1 | |
---4 A car starts from rest and moves in a straight line with constant acceleration $a \mathrm {~m} \mathrm {~s} ^ { - 2 }$ for a distance of 50 m . The car then travels with constant velocity for 500 m for a period of 25 s , before decelerating to rest. The magnitude of this deceleration is $2 a \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Sketch the velocity-time graph for the motion of the car.\\
\includegraphics[max width=\textwidth, alt={}, center]{55090630-1413-45cd-8201-4d58662db6bd-05_533_1155_534_534}
\item Find the value of $a$.
\item Find the total time for which the car is in motion.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q4 [7]}}