A marine salvage ROV (Remotely Operated Vehicle) of mass 2.5 kg is operating at depth. Its motion is governed by two horizontal thruster forces P1\mathbf{P}_1P1 and P2\mathbf{P}_2P2 such that:
P1=(3a−11) N and P2=(52b) N \mathbf{P}_1 = \begin{pmatrix} 3a \\ -11 \end{pmatrix} \text{ N and } \mathbf{P}_2 = \begin{pmatrix} 5 \\ 2b \end{pmatrix} \text{ N} P1=(3a−11) N and P2=(52b) Nwhere a a\,a and b b\,b are constant parameters. The resulting acceleration of the ROV is observed to be a=(2ba−1) m s−2\mathbf{a} = \begin{pmatrix} 2b \\ a - 1 \end{pmatrix} \text{ m s}^{-2}a=(2ba−1) m s−2.
Determine the value of a a\,a and the value of bbb.
265 exam-style questions on AQA A Level Maths 3.2 Q: Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Constant acceleration formulae, 3.2.4 Calculus in kinematics (A-level only), and 3.2.5 Motion under gravity and projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.