| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Find velocity by integrating acceleration |
| Difficulty | Moderate -0.3 This is a straightforward vector mechanics question requiring direct substitution into given formulae, application of F=ma, and integration of acceleration to find velocity with one constant to determine. All steps are routine M1 techniques with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 3.02g Two-dimensional variable acceleration3.03d Newton's second law: 2D vectors |
5 The acceleration of a particle of mass 4 kg is given by $\mathbf { a } = ( 9 \mathbf { i } - 4 t \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }$, where $\mathbf { i }$ and $\mathbf { j }$ are unit vectors and $t$ is the time in seconds.\\
(i) Find the acceleration of the particle when $t = 0$ and also when $t = 3$.\\
(ii) Calculate the force acting on the particle when $t = 3$.
The particle has velocity $( 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ when $t = 1$.\\
(iii) Find an expression for the velocity of the particle at time $t$.
\hfill \mbox{\textit{OCR MEI M1 2006 Q5 [6]}}