A team of marine engineers is testing two autonomous underwater vehicles (AUVs), Alpha and Beta, along a 200-metre straight section of a subsea pipeline. Both AUVs are launched from a stationary position at the start of the section.
The acceleration, a m s−2a\text{ m s}^{-2}a m s−2, of each AUV is modeled as a function of time, t t\,t seconds, after the launch command is issued:
Acceleration of Alpha: aA=0.048t2 \text{Acceleration of Alpha: } a_A = 0.048t^2 Acceleration of Alpha: aA=0.048t2 Acceleration of Beta: aB=0.0125t3 \text{Acceleration of Beta: } a_B = 0.0125t^3 Acceleration of Beta: aB=0.0125t3Calculate the time taken for AUV Alpha to traverse the 200-metre section. Give your answer to four significant figures.
The engineers intend to deploy the AUV that completes the 200-metre distance in the least amount of time. Determine which AUV should be deployed based on these models.
The models assume that both AUVs respond instantaneously to the launch command at t=0t = 0t=0. In reality, there is a signal propagation delay through the water. Explain why this might invalidate the choice made in part (b).
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.