A search-and-rescue drone is deployed to locate a radio signal. At time ttt seconds, its position vector r\mathbf{r}r metres, relative to a fixed base station, is given by
[r=(23t3−5t2+12)i+(20t−2t2−7)j [\mathbf{r} = \left(\frac{2}{3}t^3 - 5t^2 + 12\right)\mathbf{i} + (20t - 2t^2 - 7)\mathbf{j} [r=(32t3−5t2+12)i+(20t−2t2−7)jCalculate the exact speed of the drone when t=4t = 4t=4.
An analyst suggests that the magnitude of the drone's acceleration will never fall to zero. Determine, with full justification, whether the analyst is correct.
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.