A survey drone is programmed to follow a path in a horizontal plane such that its position vector r\mathbf{r}r metres, at time t t\,t seconds, is given by
r=(2t2−13t3)i+(10−5t−32t2)j \mathbf{r} = \left(2t^2 - \frac{1}{3}t^3\right)\mathbf{i} + \left(10 - 5t - \frac{3}{2}t^2\right)\mathbf{j} r=(2t2−31t3)i+(10−5t−23t2)jrelative to a fixed origin.
Find the exact speed of the drone when t=3t = 3t=3.
An engineer suggests that the magnitude of the drone's acceleration will be zero at some time t>0t > 0t>0. Determine whether the engineer's claim is correct. Fully justify your answer.
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.