At time t t\,t seconds a particle P P\,P has velocity v\mathbf{v}v m s−1^{-1}−1, where v=3t12i−2tj\displaystyle \mathbf{v} = 3t^{\frac{1}{2}}\mathbf{i} - 2t\mathbf{j}v=3t21i−2tj.
When t=1t = 1t=1, P P\,P is at the point AAA. When t=4t = 4t=4, P P\,P is at the point BBB.
Find the exact distance ABABAB.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.