A particle has an initial velocity of (3i−8j) ms−1(3\mathbf{i} - 8\mathbf{j}) \text{ ms}^{-1}(3i−8j) ms−1 and is accelerating uniformly in the direction (2i+j)(2\mathbf{i} + \mathbf{j})(2i+j) where i\mathbf{i}i and j\mathbf{j}j are perpendicular unit vectors. Given that the magnitude of the acceleration is 45 ms−24\sqrt{5} \text{ ms}^{-2}45 ms−2,
show that, after t t\,t seconds, the velocity vector of the particle is [(8t+3)i+(4t−8)j] ms−1[(8t + 3)\mathbf{i} + (4t - 8)\mathbf{j}] \text{ ms}^{-1}[(8t+3)i+(4t−8)j] ms−1.
Using your answer to part (a), or otherwise, find the value of t t\,t for which the speed of the particle is at its minimum.
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.