At time t=0t = 0t=0, a particle has a velocity of (3i−7j) ms−1(3\mathbf{i} - 7\mathbf{j}) \text{ ms}^{-1}(3i−7j) ms−1. It moves with a constant acceleration of magnitude 45 ms−24\sqrt{5} \text{ ms}^{-2}45 ms−2 in the direction (i+2j)(\mathbf{i} + 2\mathbf{j})(i+2j).
Show that the velocity of the particle at time t t\,t is given by v=[(4t+3)i+(8t−7)j] ms−1\mathbf{v} = [(4t + 3)\mathbf{i} + (8t - 7)\mathbf{j}] \text{ ms}^{-1}v=[(4t+3)i+(8t−7)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.
