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.
