| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2010 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Displacement expressions and comparison |
| Difficulty | Standard +0.3 Part (i) is a straightforward SUVAT calculation requiring one standard formula. Part (ii) involves integrating a linear acceleration function twice and verifying equality, which is routine calculus for M1 but slightly more involved than pure recall. Overall slightly easier than average due to clear structure and standard techniques. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02f Non-uniform acceleration: using differentiation and integration |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \((1.5 + 3.5)/2 = s/10\) | B1 | For using \(\frac{u+v}{2} = \frac{s}{t}\) |
| Displacement is 25 m | B1 | [2] |
| (ii) For using \(v = \int adt\) | M1 | |
| \(v = 0.015t^2(+ C)\) | A1 | |
| \([3.5 = 0.015 \times 100 + C \rightarrow C = 2]\) | B1 | |
| \([s = 0.005t^3 + 2t + (0)]\) | M1 | For using \(s = \int vdt\) |
| Displacement is 25 m, same as P. | A1 | [5] |
**(i)** $(1.5 + 3.5)/2 = s/10$ | B1 | For using $\frac{u+v}{2} = \frac{s}{t}$
Displacement is 25 m | B1 | [2]
**(ii)** For using $v = \int adt$ | M1 |
$v = 0.015t^2(+ C)$ | A1 |
$[3.5 = 0.015 \times 100 + C \rightarrow C = 2]$ | B1 |
$[s = 0.005t^3 + 2t + (0)]$ | M1 | For using $s = \int vdt$
Displacement is 25 m, same as P. | A1 | [5]4 A particle $P$ starts from a fixed point $O$ at time $t = 0$, where $t$ is in seconds, and moves with constant acceleration in a straight line. The initial velocity of $P$ is $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and its velocity when $t = 10$ is $3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Find the displacement of $P$ from $O$ when $t = 10$.
Another particle $Q$ also starts from $O$ when $t = 0$ and moves along the same straight line as $P$. The acceleration of $Q$ at time $t$ is $0.03 t \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(ii) Given that $Q$ has the same velocity as $P$ when $t = 10$, show that it also has the same displacement from $O$ as $P$ when $t = 10$.
\hfill \mbox{\textit{CAIE M1 2010 Q4 [7]}}