| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Find velocity from position |
| Difficulty | Standard +0.3 This is a straightforward vector mechanics question requiring differentiation of position to find velocity and acceleration, plus basic vector calculations (bearing from components). All steps are routine M1 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.10b Vectors in 3D: i,j,k notation3.02e Two-dimensional constant acceleration: with vectors3.02f Non-uniform acceleration: using differentiation and integration |
4 At time $t$ seconds, a particle has position with respect to an origin O given by the vector
$$\mathbf { r } = \binom { 8 t } { 10 t ^ { 2 } - 2 t ^ { 3 } } ,$$
where $\binom { 1 } { 0 }$ and $\binom { 0 } { 1 }$ are perpendicular unit vectors east and north respectively and distances are in metres.\\
(i) When $t = 1$, the particle is at P . Find the bearing of P from O .\\
(ii) Find the velocity of the particle at time $t$ and show that it is never zero.\\
(iii) Determine the time(s), if any, when the acceleration of the particle is zero.
\hfill \mbox{\textit{OCR MEI M1 2011 Q4 [8]}}