A particle has initial velocity (i−5j)(\mathbf{i} - 5\mathbf{j})(i−5j) m s−1^{-1}−1 and accelerates 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.
The magnitude of the acceleration is 35 3\sqrt{5}\,35 m s−2^{-2}−2.
Show that after t t\,t seconds the velocity of the particle is [(6t+1)i+(3t−5)j]\left[(6t + 1)\mathbf{i} + (3t - 5)\mathbf{j}\right][(6t+1)i+(3t−5)j] m s−1^{-1}−1.
Using your answer to part (a), or otherwise, find the value of t t\,t for which the speed of the particle is least.