A particle P P\,P moves with constant acceleration 3i−4j ms−23\mathbf{i} - 4\mathbf{j} \text{ ms}^{-2}3i−4j ms−2. When t=0t = 0t=0, the particle is at the origin, OOO, and moving with a velocity 2i−2j ms−12\mathbf{i} - 2\mathbf{j} \text{ ms}^{-1}2i−2j ms−1. At time t=Tt = Tt=T seconds, where T>0T > 0T>0, P P\,P passes through the point AAA. The position vector of A A\,A is ki−12j mk\mathbf{i} - 12\mathbf{j} \text{ m}ki−12j m relative to OOO, where k k\,k is a constant.
Find the value of TTT.
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.