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.
