| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Particle on inclined plane |
| Difficulty | Standard +0.3 This is a standard SUVAT problem on an inclined plane with constant acceleration. Part (i) requires applying s=ut+½at² to two segments to find deceleration and initial speed—straightforward algebra with given numerical values. Part (ii) involves resolving forces parallel to the plane (mg sin θ + friction = ma), which is routine M1 content. The question is slightly above average due to the two-stage calculation and force resolution, but follows standard textbook methods without requiring novel insight. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | For using constant acceleration equations such as \(s = ut + \frac{1}{2}at^2\) or equivalent complete methods to find expressions for \(PQ\) or \(QR\) or \(PR\) | |
| For \(PQ\): \(0.8 = 0.6u + 0.18a\) | A1 | |
| For \(PR\): \(1.6 = 1.6u + 1.28a\) | A1 | or for \(QR\): \(0.8 = (u + a \times 0.6) \times 1 + 0.5a\) |
| M1 | Solving simultaneously two relevant equations in \(u\) and \(a\) | |
| Deceleration \(= \frac{2}{3}\text{ ms}^{-2}\) | A1 | AG |
| \(u = \frac{23}{15}\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(R = mg\cos 3\) | B1 | |
| \(F = \mu mg\cos 3\) | M1 | For use of \(F = \mu R\) |
| \(-mg\sin 3 - \mu \times mg\cos 3 = m \times \left(-\frac{2}{3}\right)\) | M1 | For using Newton's second law (3 terms) |
| \(\mu = 0.0144\ (0.014350\ldots)\) | A1 |
## Question 6(i):
| | M1 | For using constant acceleration equations such as $s = ut + \frac{1}{2}at^2$ or equivalent complete methods to find expressions for $PQ$ or $QR$ or $PR$ |
|---|---|---|
| For $PQ$: $0.8 = 0.6u + 0.18a$ | A1 | |
| For $PR$: $1.6 = 1.6u + 1.28a$ | A1 | or for $QR$: $0.8 = (u + a \times 0.6) \times 1 + 0.5a$ |
| | M1 | Solving simultaneously two relevant equations in $u$ and $a$ |
| Deceleration $= \frac{2}{3}\text{ ms}^{-2}$ | A1 | AG |
| $u = \frac{23}{15}$ | B1 | |
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## Question 6(ii):
| $R = mg\cos 3$ | B1 | |
|---|---|---|
| $F = \mu mg\cos 3$ | M1 | For use of $F = \mu R$ |
| $-mg\sin 3 - \mu \times mg\cos 3 = m \times \left(-\frac{2}{3}\right)$ | M1 | For using Newton's second law (3 terms) |
| $\mu = 0.0144\ (0.014350\ldots)$ | A1 | |
---6 A particle is projected from a point $P$ with initial speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ up a line of greatest slope $P Q R$ of a rough inclined plane. The distances $P Q$ and $Q R$ are both equal to 0.8 m . The particle takes 0.6 s to travel from $P$ to $Q$ and 1 s to travel from $Q$ to $R$.\\
(i) Show that the deceleration of the particle is $\frac { 2 } { 3 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and hence find $u$, giving your answer as an exact fraction.\\
(ii) Given that the plane is inclined at $3 ^ { \circ }$ to the horizontal, find the value of the coefficient of friction between the particle and the plane.\\
\hfill \mbox{\textit{CAIE M1 2018 Q6 [10]}}