A high-precision calibration glider of mass 0.4 kg is being manipulated on a horizontal low-friction air-table. Two magnetic actuators exert forces F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2 on the glider, where:
F1=[2a1.8] N and F2=[−3b] N \mathbf{F}_1 = \begin{bmatrix} 2a \\ 1.8 \end{bmatrix} \text{ N and } \mathbf{F}_2 = \begin{bmatrix} -3 \\ b \end{bmatrix} \text{ N} F1=[2a1.8] N and F2=[−3b] Nand a,b a, b\,a,b are constants. The glider's resulting acceleration vector is given by a=[5b10a] m s−2\mathbf{a} = \begin{bmatrix} 5b \\ 10a \end{bmatrix} \text{ m s}^{-2}a=[5b10a] 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.