| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Find acceleration from distances/times |
| Difficulty | Moderate -0.3 This is a straightforward SUVAT question requiring application of v² = u² + 2as twice, then algebraic manipulation to eliminate 'a'. While it involves multiple steps and algebraic unknowns, the approach is standard and mechanical—students simply apply a familiar formula twice and solve simultaneously. Slightly easier than average due to the clear structure and routine nature of the technique. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (a) \(7^2 - 5^2 = 2ad_1\) | M1 | For using \(v^2 = u^2 + 2as\) |
| (b) \(8^2 - 7^2 = 2ad_2\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\frac{24}{15} = \frac{d_1}{d_2}\) | M1 | For eliminating \(a\) |
| \(d_1 = 1.6d_2\) | A1 |
## Question 1:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| (a) $7^2 - 5^2 = 2ad_1$ | M1 | For using $v^2 = u^2 + 2as$ |
| (b) $8^2 - 7^2 = 2ad_2$ | A1 | |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{24}{15} = \frac{d_1}{d_2}$ | M1 | For eliminating $a$ |
| $d_1 = 1.6d_2$ | A1 | |
---1 A car travels in a straight line with constant acceleration $a \mathrm {~m} \mathrm {~s} ^ { - 2 }$. It passes the points $A , B$ and $C$, in this order, with speeds $5 \mathrm {~m} \mathrm {~s} ^ { - 1 } , 7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. The distances $A B$ and $B C$ are $d _ { 1 } \mathrm {~m}$ and $d _ { 2 } \mathrm {~m}$ respectively.\\
(i) Write down an equation connecting
\begin{enumerate}[label=(\alph*)]
\item $d _ { 1 }$ and $a$,
\item $d _ { 2 }$ and $a$.\\
(ii) Hence find $d _ { 1 }$ in terms of $d _ { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2005 Q1 [4]}}