| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| 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 problem requiring systematic application of kinematic equations with two unknowns (initial velocity and acceleration). Part (i) involves setting up two equations from s=ut+½at² for the two segments, then solving simultaneously—a standard technique. Part (ii) is a direct application of v²=u²+2as once the velocity at C is known. While it requires careful algebraic manipulation and multiple steps, it follows a well-practiced procedure with no conceptual surprises, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(100 = 4u + 8a\) or \(100 = \frac{1}{2}(u+v)\times 4\) or \(148 = 4v + 8a\) or any equation in two of the variables \(u, v, w, a\) | M1 | Any relevant use of constant acceleration equations in any two of the variables: \(a\) is acceleration, \(u\) is speed at \(A\), \(v\) is speed at \(B\), \(w\) is speed at \(C\) |
| One correct equation | A1 | |
| \(248 = 8u + 32a\) or two further correct equations in 3 unknowns such as \(148 = 4v + 8a\) and \(v = u + 4a\) or \(148 = \frac{1}{2}(v+w)\times 4\) and \(248 = \frac{1}{2}(u+w)\times 8\) | A1 | A second correct equation in the same two variables, or two further correct equations leading to three equations in three of the unknowns \(u, v, w, a\) |
| M1 | Attempt to solve for \(a\) or \(u\); must reach \(a = \ldots\) or \(u = \ldots\) | |
| \(a = 3\) | A1 | AG |
| \(u = 19\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(61^2 = 19^2 + 2\times 3\times s\) | M1 | Attempt equation for \(s = AD\) |
| \([s = 560 \rightarrow CD = 560 - 248]\) | M1 | Attempt to find \(CD\) |
| Distance \(CD\) is 312 | A1 | |
| Alternative: Speed at \(C\) is \(19 + 8\times 3\ [= 43]\) | M1 | Attempt to find speed at \(C\) |
| \([61^2 = 43^2 + 2\times 3\times CD]\) | M1 | Attempt to find \(CD\) |
| Distance \(CD\) is 312 | A1 |
## Question 4(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $100 = 4u + 8a$ or $100 = \frac{1}{2}(u+v)\times 4$ or $148 = 4v + 8a$ or any equation in two of the variables $u, v, w, a$ | M1 | Any relevant use of constant acceleration equations in any two of the variables: $a$ is acceleration, $u$ is speed at $A$, $v$ is speed at $B$, $w$ is speed at $C$ |
| One correct equation | A1 | |
| $248 = 8u + 32a$ or two further correct equations in 3 unknowns such as $148 = 4v + 8a$ and $v = u + 4a$ or $148 = \frac{1}{2}(v+w)\times 4$ and $248 = \frac{1}{2}(u+w)\times 8$ | A1 | A second correct equation in the same two variables, or two further correct equations leading to three equations in three of the unknowns $u, v, w, a$ |
| | M1 | Attempt to solve for $a$ or $u$; must reach $a = \ldots$ or $u = \ldots$ |
| $a = 3$ | A1 | AG |
| $u = 19$ | B1 | |
---
## Question 4(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $61^2 = 19^2 + 2\times 3\times s$ | M1 | Attempt equation for $s = AD$ |
| $[s = 560 \rightarrow CD = 560 - 248]$ | M1 | Attempt to find $CD$ |
| Distance $CD$ is 312 | A1 | |
| **Alternative:** Speed at $C$ is $19 + 8\times 3\ [= 43]$ | M1 | Attempt to find speed at $C$ |
| $[61^2 = 43^2 + 2\times 3\times CD]$ | M1 | Attempt to find $CD$ |
| Distance $CD$ is 312 | A1 | |
---4 A particle $P$ moves in a straight line $A B C D$ with constant acceleration. The distances $A B$ and $B C$ are 100 m and 148 m respectively. The particle takes 4 s to travel from $A$ to $B$ and also takes 4 s to travel from $B$ to $C$.\\
(i) Show that the acceleration of $P$ is $3 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and find the speed of $P$ at $A$.\\
(ii) $P$ reaches $D$ with a speed of $61 \mathrm {~ms} ^ { - 1 }$. Find the distance $C D$.\\
\hfill \mbox{\textit{CAIE M1 2018 Q4 [9]}}