Two forces F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2 act on a particle of mass 2 kg.
It is given that F1=(ai+8j)\mathbf{F}_1 = (a\mathbf{i} + 8\mathbf{j})F1=(ai+8j) N and F2=(5i+bj)\mathbf{F}_2 = (5\mathbf{i} + b\mathbf{j})F2=(5i+bj) N where a a\,a and b b\,b are constants.
The particle has acceleration (bi+aj)(b\mathbf{i} + a\mathbf{j})(bi+aj) m s−2^{-2}−2.
Show that a+5=2ba + 5 = 2ba+5=2b and that 8+b=2a8 + b = 2a8+b=2a.
Hence find the value of a a\,a and the value of bbb.
139 exam-style questions on AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.