| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Constant acceleration with algebraic unknowns |
| Difficulty | Standard +0.3 This is a standard kinematics problem requiring application of SUVAT equations with two constraints (equal distances AB=BC, different times). The 'show that' format guides students to the answer, and the method is straightforward once the correct equations are set up. Slightly above average due to the algebraic manipulation needed, but well within typical M1 scope. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| 3(i) | s = 14 × 5 + ½a × 52 | |
| AB | B1 | or s = ½(14 + 14 + 5a) × 5 OE |
| Answer | Marks | Guidance |
|---|---|---|
| AC | B1 | or s = ½(14 + 14 + 8a) × 8 OE |
| Answer | Marks | Guidance |
|---|---|---|
| [112 + 32a = 2(70 + 12.5a)] | M1 | Using AC = 2AB and solving for a or for |
| Answer | Marks | Guidance |
|---|---|---|
| a = 4 m s–2 | A1 | AG, If substituting a = 4 must show |
| Answer | Marks | Guidance |
|---|---|---|
| 3(ii) | [v = 14 + 4 × 8] | M1 |
| Answer | Marks |
|---|---|
| Velocity = 46 m s-1 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(i) ---
3(i) | s = 14 × 5 + ½a × 52
AB | B1 | or s = ½(14 + 14 + 5a) × 5 OE
AB
s = 14 × 8 + ½a × 82
AC | B1 | or s = ½(14 + 14 + 8a) × 8 OE
AC
[112 + 32a = 2(70 + 12.5a)] | M1 | Using AC = 2AB and solving for a or for
substituting a = 4 and finding AB and AC
a = 4 m s–2 | A1 | AG, If substituting a = 4 must show
AB = 120 and AC = 240 OE
4
--- 3(ii) ---
3(ii) | [v = 14 + 4 × 8] | M1 | Use of v = u + at
or any complete method to find v
Velocity = 46 m s-1 | A1
2
Question | Answer | Marks | GuidanceA car travels along a straight road with constant acceleration. It passes through points $A$, $B$ and $C$. The car passes point $A$ with velocity 14 m s$^{-1}$. The two sections $AB$ and $BC$ are of equal length. The times taken to travel along $AB$ and $BC$ are 5 s and 3 s respectively.
\begin{enumerate}[label=(\roman*)]
\item Write down an expression for the distance $AB$ in terms of the acceleration of the car. Write down a similar expression for the distance $AC$. Hence show that the acceleration of the car is 4 m s$^{-2}$. [4]
\item Find the speed of the car as it passes point $C$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2017 Q3 [6]}}