A particle moves with an initial velocity of (−4i+6j) ms−1(-4\mathbf{i} + 6\mathbf{j}) \text{ ms}^{-1}(−4i+6j) ms−1 and experiences a constant acceleration in the direction of the vector (3i−4j)(3\mathbf{i} - 4\mathbf{j})(3i−4j). The magnitude of this acceleration is 10 ms-2, where i\mathbf{i}i and j\mathbf{j}j are perpendicular unit vectors.
Show that, after t t\,t seconds, the velocity vector of the particle is [(6t−4)i+(6−8t)j] ms−1[(6t - 4)\mathbf{i} + (6 - 8t)\mathbf{j}] \text{ ms}^{-1}[(6t−4)i+(6−8t)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.
158 exam-style questions on OCR (MEI) A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Position, displacement, distance and distance travelled, 3.2.3 Velocity, speed and acceleration distinctions, 3.2.4 Draw and interpret kinematics graphs, 3.2.5 Differentiate position and velocity (A-level only), 3.2.6 Integrate acceleration and velocity (A-level only), 3.2.7 When constant acceleration formulae apply, 3.2.8 Solve 1-D kinematics problems, 3.2.9 Language of kinematics in 2 dimensions (A-level only), 3.2.10 Extend 1-D techniques to 2-D using vectors (A-level only), 3.2.11 Cartesian equation of a path (A-level only), and 3.2.12 Vectors to solve kinematics problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.