[In this question, the unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively.]
A particle P P\,P is moving with constant velocity (−5i+8j) m s−1(-5\mathbf{i} + 8\mathbf{j}) \text{ m s}^{-1}(−5i+8j) m s−1.
Find the speed of PPP.
Find the direction of motion of PPP, giving your answer as a bearing.
At time t=0t = 0t=0, P P\,P is at the point A A\,A with position vector (7i−10j) m(7\mathbf{i} - 10\mathbf{j}) \text{ m}(7i−10j) m relative to a fixed origin OOO. When t=3 st = 3 \text{ s}t=3 s, the velocity of P P\,P changes and it moves with velocity (ui+vj) m s−1(u\mathbf{i} + v\mathbf{j}) \text{ m s}^{-1}(ui+vj) m s−1, where u u\,u and v v\,v are constants. After a further 4 s, it passes through O O\,O and continues to move with velocity (ui+vj) m s−1(u\mathbf{i} + v\mathbf{j}) \text{ m s}^{-1}(ui+vj) m s−1. Find the values of u u\,u and vvv.
Find the total time taken for P P\,P to move from A A\,A to a position which is due south of AAA.
Practise Edexcel A Level Old Maths Vectors with exam-style questions for A Level Old Maths. 9 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.