| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Displacement expressions and comparison |
| Difficulty | Moderate -0.3 This is a straightforward two-part SUVAT question requiring standard application of kinematic equations (v = u + at, v² = u² + 2as) in part (i), and basic integration of a velocity function in part (ii). All steps are routine with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02f Non-uniform acceleration: using differentiation and integration |
| Answer | Marks | Guidance |
|---|---|---|
| \([5 = 2 + 0.05t\) or \(25 = 4 + 2 \times 0.05(AB)]\) | M1 | For using \(v = u + at\) or \(v^2 = u^2 + 2as\) |
| Time taken is 60 s (or Distance is 210 m) | A1 | |
| Distance is 210 m (or Time taken is 60 s) | B1 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(s = kt^4 (+C)\) | B1 | |
| \(C = 0\) (may be implied by its absence) | B1 | |
| \([210 = k \times 60^3/4]\) | M1 | For using \(s = 210\) when \(t = 60\) |
| \(k = 7/1080000\) or 0.0000648 | A1 | |
| Speed of Q at B is 14 ms\(^{-1}\) | B1 ft | 5 |
**(i)**
$[5 = 2 + 0.05t$ or $25 = 4 + 2 \times 0.05(AB)]$ | M1 | For using $v = u + at$ or $v^2 = u^2 + 2as$
Time taken is 60 s (or Distance is 210 m) | A1 |
Distance is 210 m (or Time taken is 60 s) | B1 | 3
**(ii)**
$s = kt^4 (+C)$ | B1 |
$C = 0$ (may be implied by its absence) | B1 |
$[210 = k \times 60^3/4]$ | M1 | For using $s = 210$ when $t = 60$
$k = 7/1080000$ or 0.0000648 | A1 |
Speed of Q at B is 14 ms$^{-1}$ | B1 ft | 5 | If $k \times 60^3$5 Particle $P$ travels along a straight line from $A$ to $B$ with constant acceleration $0.05 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. Its speed at $A$ is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and its speed at $B$ is $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Find the time taken for $P$ to travel from $A$ to $B$, and find also the distance $A B$.
Particle $Q$ also travels along the same straight line from $A$ to $B$, starting from rest at $A$. At time $t \mathrm {~s}$ after leaving $A$, the speed of $Q$ is $k t ^ { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$, where $k$ is a constant. $Q$ takes the same time to travel from $A$ to $B$ as $P$ does.\\
(ii) Find the value of $k$ and find $Q$ 's speed at $B$.
\hfill \mbox{\textit{CAIE M1 2012 Q5 [8]}}