Motion in two dimensions with vectorsAQA A-Level Maths: Mind map

Exam questions on Motion in two dimensions with vectors

1. A particle $P$ moves in a horizontal plane with constant acceleration $(2\mathbf i-\mathbf j)$ m s$^{-2}$, where $\mathbf i$ and $\mathbf j$ are perpendicular unit vectors. At time $t=0$ the velocity of $P$ is $(\mathbf i+3\mathbf j)$ m s$^{-1}$ and its position vector relative to a fixed origin $O$ is $(3\mathbf i+4\mathbf j)$ m.
   Find the speed of $P$ when $t=2$.2 marks
2. A particle moves in a plane so that at time $t$ seconds its position vector relative to a fixed origin $O$ is $\mathbf r=\left[(t^3-3t)\mathbf i+(4t-t^2)\mathbf j\right]$ m, where $\mathbf i$ and $\mathbf j$ are perpendicular unit vectors.
   Find the value of $t$ at which the particle is moving parallel to $\mathbf i$.2 marks
3. A particle moves in a plane with acceleration $\mathbf a=(4t\,\mathbf i-2\mathbf j)$ m s$^{-2}$ at time $t$ seconds, where $\mathbf i$ and $\mathbf j$ are perpendicular unit vectors. When $t=0$ the velocity of the particle is $(2\mathbf i+5\mathbf j)$ m s$^{-1}$ and its position vector relative to a fixed origin $O$ is $(\mathbf i+3\mathbf j)$ m.
   Find the velocity of the particle at time $t$.3 marks