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.
158 exam-style questions on OCR (MEI) A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Position, displacement, distance and distance travelled, 3.2.3 Velocity, speed and acceleration distinctions, 3.2.4 Draw and interpret kinematics graphs, 3.2.5 Differentiate position and velocity (A-level only), 3.2.6 Integrate acceleration and velocity (A-level only), 3.2.7 When constant acceleration formulae apply, 3.2.8 Solve 1-D kinematics problems, 3.2.9 Language of kinematics in 2 dimensions (A-level only), 3.2.10 Extend 1-D techniques to 2-D using vectors (A-level only), 3.2.11 Cartesian equation of a path (A-level only), and 3.2.12 Vectors to solve kinematics problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.