Displacement, velocity, acceleration and force as vectorsEdexcel International A Level Maths: Mind map

Exam questions on Displacement, velocity, acceleration and force as vectors

1. A particle moves in a horizontal plane with constant velocity $(3\mathbf{i}-4\mathbf{j})$ m s$^{-1}$, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in the directions east and north. At time $t=0$ its position vector relative to a fixed origin $O$ is $(2\mathbf{i}+5\mathbf{j})$ m.
   Find the position vector of the particle at $t=6$ s.2 marks
2. A particle moves in a plane with constant acceleration. At time $t=0$ its velocity is $(2\mathbf{i}+\mathbf{j})$ m s$^{-1}$ and 4 s later its velocity is $(14\mathbf{i}-8\mathbf{j})$ m s$^{-1}$, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
   Find the magnitude of the acceleration.2 marks
3. Relative to a fixed origin $O$, a ship $S$ moves with constant velocity $(4\mathbf{i}+3\mathbf{j})$ km h$^{-1}$, where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors due east and due north. At time $t=0$ (hours) the ship is at the point with position vector $(-8\mathbf{i}-5\mathbf{j})$ km. A lighthouse $L$ is at the point with position vector $(12\mathbf{i}+4\mathbf{j})$ km.
   Find the position vector of $S$ at time $t$ hours. Hence find the distance of $S$ from $O$ when $t=2$.3 marks