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)i
where 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.
Practise Edexcel A Level Maths Further Kinematics with exam-style questions for A Level Maths. 54 questions covering Vectors in Kinematics, Vector Methods with Projectiles, Variable Acceleration in One Dimension, Differentiating Vectors, and Integrating Vectors, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.