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).
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.