A particle P P\,P moves with constant acceleration i−j\mathbf{i} - \mathbf{j}i−j ms−2^{-2}−2. When t=0t = 0t=0, the particle is at point A A\,A and moving with a velocity −2i+3j-2\mathbf{i} + 3\mathbf{j}−2i+3j ms−1^{-1}−1. At time t=Tt = Tt=T the particle is moving in the direction of vector (−i+2j)(-\mathbf{i} + 2\mathbf{j})(−i+2j).
Show that the velocity of P P\,P at time t t\,t is (−2+t)i+(3−t)j(-2 + t)\mathbf{i} + (3 - t)\mathbf{j}(−2+t)i+(3−t)j.
Find the value of TTT.
At time t=2t = 2t=2 seconds, P P\,P is at the point BBB. Find the distance ABABAB.
363 exam-style questions on Edexcel A Level Maths Further Kinematics, covering 8.1 Vectors in Kinematics, 8.2 Vector Methods with Projectiles, 8.3 Variable Acceleration in One Dimension, 8.4 Differentiating Vectors, and 8.5 Integrating Vectors. Each one has a worked solution and a mark scheme showing where the marks go.