Standard +0.3 This question requires understanding that bearing 045° means equal i and j components, leading to a simple quadratic equation. The multi-step nature (equating components, solving quadratic, finding speed) and vector context add slight complexity beyond routine problems, but the mathematical techniques are standard M1 material with no novel insight required.
4 The directions of the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are east and north.
The velocity of a particle, \(\mathrm { vm } \mathrm { s } ^ { - 1 }\), at time \(t \mathrm {~s}\) is given by
$$\mathbf { v } = \left( 16 - t ^ { 2 } \right) \mathbf { i } + ( 31 - 8 t ) \mathbf { j } .$$
Find the time at which the particle is travelling on a bearing of \(045 ^ { \circ }\) and the speed of the particle at this time.
4 The directions of the unit vectors $\mathbf { i }$ and $\mathbf { j }$ are east and north.\\
The velocity of a particle, $\mathrm { vm } \mathrm { s } ^ { - 1 }$, at time $t \mathrm {~s}$ is given by
$$\mathbf { v } = \left( 16 - t ^ { 2 } \right) \mathbf { i } + ( 31 - 8 t ) \mathbf { j } .$$
Find the time at which the particle is travelling on a bearing of $045 ^ { \circ }$ and the speed of the particle at this time.
\hfill \mbox{\textit{OCR MEI M1 2013 Q4 [6]}}