At time t t\,t seconds a particle P P\,P has position vector r=[(t2+5t−2)i+(t3+2t2)j]\mathbf{r} = \left[(t^2 + 5t - 2)\mathbf{i} + (t^3 + 2t^2)\mathbf{j}\right]r=[(t2+5t−2)i+(t3+2t2)j] m.
Find the position vector of P P\,P when t=2t = 2t=2.
Find the velocity of P P\,P when t=3t = 3t=3.
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.