| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Finding when particle at rest |
| Difficulty | Standard +0.3 This is a straightforward mechanics question requiring integration of a polynomial velocity function to find distance, solving a cubic equation (which factorises nicely), and differentiating to find acceleration then solving a quadratic inequality. All techniques are standard M1 content with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration |
6 A particle travels in a straight line from a point $P$ to a point $Q$. Its velocity $t$ seconds after leaving $P$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, where $v = 4 t - \frac { 1 } { 16 } t ^ { 3 }$. The distance $P Q$ is 64 m .\\
(i) Find the time taken for the particle to travel from $P$ to $Q$.\\
(ii) Find the set of values of $t$ for which the acceleration of the particle is positive.
\hfill \mbox{\textit{CAIE M1 2011 Q6 [9]}}