A particle P P\,P has acceleration [(3t−3)i+(2t−4)j] ms−2[(3t - 3)\mathbf{i} + (2t - 4)\mathbf{j}] \text{ ms}^{-2}[(3t−3)i+(2t−4)j] ms−2 where t t\,t is the time in seconds. Initially P P\,P has velocity (3i+5j) ms−1(3\mathbf{i} + 5\mathbf{j}) \text{ ms}^{-1}(3i+5j) ms−1. The velocity of P P\,P is [(32t2−3t+3)i+(t2−4t+5)j] ms−1\displaystyle [(\frac{3}{2}t^2 - 3t + 3)\mathbf{i} + (t^2 - 4t + 5)\mathbf{j}] \text{ ms}^{-1}[(23t2−3t+3)i+(t2−4t+5)j] ms−1
Find the velocities at the two times P P\,P is moving parallel to the vector (3i+j)(3\mathbf{i} + \mathbf{j})(3i+j)
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.