An engineer is comparing the performance of two prototype electric vehicles, X and Y, along a straight test track. Both vehicles start from rest.
The acceleration, in m s−2\text{m s}^{-2}m s−2, of each vehicle is modeled as a function of time, ttt seconds, after the starting signal:
Acceleration of X=0.162t2 \text{Acceleration of X} = 0.162t^2 Acceleration of X=0.162t2 Acceleration of Y=0.045t3 \text{Acceleration of Y} = 0.045t^3 Acceleration of Y=0.045t3Find the time taken for vehicle X to travel 120 metres. Give your answer to four significant figures.
The engineer recommends the vehicle that covers the 120-metre distance in the shorter time. Determine which vehicle should be recommended.
The models assume that both vehicles respond instantaneously to the signal at t=0t = 0t=0. In light of this, explain why the engineer's recommendation 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.