Final answer:
Determining which car is ahead just after leaving the starting point involves comparing car A's position, which is linear in time, to car B's, which is initially negligible. Car A, therefore, is ahead immediately after starting due to its initial velocity.
Step-by-step explanation:
To determine which car is ahead just after they leave the starting point, we compare their positions at a very small time after t=0. We are given the positions as a function of time for car A and car B, respectively: xa(t) = αt + βt2 and xb(t) = γt2 − δt3, with given constants α, β, γ, and δ. Right after starting, we can assume a very small time 't', so the terms involving t3 and t2 will be negligible compared to the terms involving 't'.
Thus, right after starting:
Position of car A (xa(t)) is approximately equal to αt since βt2 is negligible.
Position of car B (xb(t)) is approximately zero since both γt2 and δt3 are negligible.
With the given values of α = 2.60m/s and the others nonzero, car A's initial velocity of 2.60m/s is greater than car B's initial velocity of 0m/s. Therefore, car A is ahead just after they leave the starting point.