| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Finding when particle at rest |
| Difficulty | Moderate -0.8 This is a straightforward mechanics question requiring basic calculus skills: finding when v=0 by solving a simple quadratic, then integrating velocity to find displacement. Both parts are routine applications of standard techniques with no conceptual challenges or problem-solving insight required. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits3.02a Kinematics language: position, displacement, velocity, acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Time taken is \(100\) s | A1 | 2 |
| (ii) \(\frac{\dot{t}}{2} - \frac{t^3}{300}\) | M1 | For attempting to integrate \(y(t)\) |
| Distance \(AB\) is \(1670\) m (\(1666\frac{2}{3}\)) | A1 | 3 |
**(i)** Time taken is $100$ s | A1 | 2 | For attempting to solve $x(t) = 0$ |
**(ii)** $\frac{\dot{t}}{2} - \frac{t^3}{300}$ | M1 | For attempting to integrate $y(t)$ |
Distance $AB$ is $1670$ m ($1666\frac{2}{3}$) | A1 | 3 |
---2 A motorcyclist starts from rest at $A$ and travels in a straight line until he comes to rest again at $B$. The velocity of the motorcyclist $t$ seconds after leaving $A$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, where $v = t - 0.01 t ^ { 2 }$. Find\\
(i) the time taken for the motorcyclist to travel from $A$ to $B$,\\
(ii) the distance $A B$.
\hfill \mbox{\textit{CAIE M1 2006 Q2 [5]}}