| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with all parameters given |
| Difficulty | Moderate -0.3 This is a standard kinematics problem using constant acceleration equations and travel graphs. Part (a) requires calculating distances using SUVAT equations for three phases of motion for each cyclist—straightforward but multi-step. Part (b) involves setting up an equation and solving for a parameter. While it requires careful bookkeeping across multiple motion phases, the techniques are routine for M1 students with no novel problem-solving insight needed. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| 4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw). |
| Answer | Marks | Guidance |
|---|---|---|
| 4(a) | [ ] | |
| Isabella v=5×1.1 =5.5 | B1 | Isabella’s constant speed for 10 seconds |
| Use of s = ut + ½at2 or use of v–t graph to find total distance | M1 | For either Isabella or Maria, all sections included but allow one |
| Answer | Marks | Guidance |
|---|---|---|
| I 2 | A1 | For correct expression for Isabella, accept unsimplified |
| Answer | Marks | Guidance |
|---|---|---|
| M 2 | A1 | For correct expression for Maria, accept unsimplified |
| Answer | Marks |
|---|---|
| further | B1 |
| Answer | Marks |
|---|---|
| 4(b) | 1 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | M1 | Attempt total distance travelled by Isabella and set up an equation |
| Answer | Marks |
|---|---|
| a = 1.2 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 4:
4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
--- 4(a) ---
4(a) | [ ]
Isabella v=5×1.1 =5.5 | B1 | Isabella’s constant speed for 10 seconds
Use of s = ut + ½at2 or use of v–t graph to find total distance | M1 | For either Isabella or Maria, all sections included but allow one
error in use of formulae
1 1 [ ]
s = ×1.1×52 +10×5.5+ ×1.1×52 =82.5
I 2 2
or s = 1 ×( 20+10 )×5.5 [ =82.5 ]
I 2 | A1 | For correct expression for Isabella, accept unsimplified
1 [ ]
s =27.5+5×10+ ×5×5 =90
M 2 | A1 | For correct expression for Maria, accept unsimplified
Distances for Isabella = 82.5 and Maria = 90, so Maria goes
further | B1
5
--- 4(b) ---
4(b) | 1 1
a×52 +10×5a+ a×52 =90
2 2
or 1 ×( 20+10 )×5a=90
2 | M1 | Attempt total distance travelled by Isabella and set up an equation
for a, using their value of s =90. All parts included, allow one
M
error.
a = 1.2 | A1
2
Question | Answer | Marks | GuidanceTwo cyclists, Isabella and Maria, are having a race. They both travel along a straight road with constant acceleration, starting from rest at point $A$.
Isabella accelerates for 5 s at a constant rate $a \text{ m s}^{-2}$. She then travels at the constant speed she has reached for 10 s, before decelerating to rest at a constant rate over a period of 5 s.
Maria accelerates at a constant rate, reaching a speed of $5 \text{ m s}^{-1}$ in a distance of 27.5 m. She then maintains this speed for a period of 10 s, before decelerating to rest at a constant rate over a period of 5 s.
\begin{enumerate}[label=(\alph*)]
\item Given that $a = 1.1$, find which cyclist travels further. [5]
\item Find the value of $a$ for which the two cyclists travel the same distance. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2021 Q4 [7]}}