An autonomous trolley is modelled as a particle moving on a horizontal plane. At time t t\,t seconds, where t≥0t \ge 0t≥0, its velocity is v=2i+(2t+1)j\mathbf{v} = 2\mathbf{i} + (2t + 1)\mathbf{j}v=2i+(2t+1)j m s−1^{-1}−1.
At time t=0t = 0t=0, its position vector relative to a fixed origin O O\,O is (i+3j)(\mathbf{i} + 3\mathbf{j})(i+3j) m.
Find the position vector of the trolley at time ttt.
Find the Cartesian equation of the path of the trolley.
Give one reason why this model may become unrealistic for large values of ttt.
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.