At time t t\,t seconds a particle P P\,P has position vector r=[(3t3−t+3)i+(2t2+2t−1)j]\mathbf{r} = \left[(3t^3 - t + 3)\mathbf{i} + (2t^2 + 2t - 1)\mathbf{j}\right]r=[(3t3−t+3)i+(2t2+2t−1)j] m.
Find an expression for the velocity of P P\,P in terms of ttt.
Find an expression for the acceleration of P P\,P in terms of ttt.
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.