A marine research team is testing two deep-sea probes, Alpha and Beta, by deploying them into a vertical shaft within an underwater trench. Both probes are released from rest at the water's surface.
The acceleration, in m s−2\text{m s}^{-2}m s−2, of each probe is modeled as a function of time, ttt seconds, after release:
Acceleration of Alpha=0.048t2 \text{Acceleration of Alpha} = 0.048t^2 Acceleration of Alpha=0.048t2 Acceleration of Beta=0.016t3 \text{Acceleration of Beta} = 0.016t^3 Acceleration of Beta=0.016t3Determine the time taken for probe Alpha to reach a depth of 150 metres. Give your answer to four significant figures.
The team will select the probe that reaches the 150-metre depth mark in the shortest time. Determine which probe should be selected.
The models assume that both probes respond and accelerate instantaneously at t=0t = 0t=0. In light of this, explain why the team's selection might be incorrect in practice.
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.