- \hspace{0pt} [In this question, the perpendicular unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a horizontal plane.]
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
A particle \(P\) is moving on a smooth horizontal plane.
At time \(t\) seconds \(( t \geqslant 0 )\), the position vector of \(P\), relative to a fixed point \(O\), is \(\mathbf { r }\) metres and the velocity of \(P\) is \(\mathbf { v } \mathrm { ms } ^ { - 1 }\) where
$$\mathbf { v } = \left( 4 t ^ { 2 } - 5 t \right) \mathbf { i } + ( - 10 t - 12 ) \mathbf { j }$$
When \(t = 0 , \mathbf { r } = 2 \mathbf { i } + 6 \mathbf { j }\)
- Find \(\mathbf { r }\) when \(t = 2\)
When \(t = T\) particle \(P\) is moving in the direction of the vector \(\mathbf { i } - 2 \mathbf { j }\)
- Find the value of \(T\)
- Find the exact magnitude of the acceleration of \(P\) when \(t = 2.5\)