An automated research probe is navigating through a tidal stream with an initial velocity of (7i+2j) m s−1(7\mathbf{i} + 2\mathbf{j}) \text{ m s}^{-1}(7i+2j) m s−1.
The acceleration a m s−2\mathbf{a} \text{ m s}^{-2}a m s−2 of the probe at time ttt seconds is given by
a=(15kt2−12kt+6)i \mathbf{a} = (15kt^2 - 12kt + 6)\mathbf{i} a=(15kt2−12kt+6)iwhere kkk is a constant and i\mathbf{i}i and j\mathbf{j}j are perpendicular horizontal unit vectors.
When t=3t = 3t=3, the velocity of the probe is (43i+2j) m s−1(43\mathbf{i} + 2\mathbf{j}) \text{ m s}^{-1}(43i+2j) m s−1.
Show that k=29k = \frac{2}{9}k=92.
