Final answer:
To determine the slowest constant speed the green car must maintain to catch up to the blue car, the distance covered by the blue car is determined. Then, the green car's constant speed that will allow it to cover that distance in the same time period is calculated.
Step-by-step explanation:
The task is to calculate the slowest constant speed the green car must maintain to catch up to the blue car, which starts accelerating from rest with a constant acceleration of 0.2 m/s2 just after the traffic light turns green. The green car arrives at the light 7.5 seconds later. We must find the distance the blue car travels during this time and the minimum constant speed the green car needs to maintain to catch up.
To find the distance the blue car covers in 7.5 seconds, we use the kinematic equation for uniformly accelerated motion:
dblue = 0.2 m/s2 x (7.5 s)2 / 2 = 5.625 m
The green car must cover this distance in the same time it took the blue car to cover it after 7.5 seconds to catch up. Since the blue car is still accelerating, we need to account for the total time the green car will be moving to catch up. Let's denote time from the green car's arrival at the light as t.
The total distance traveled by blue car when green catches up is:
dtotal = 5.625 m (initial 7.5 seconds) + 0.5 x 0.2 m/s2 x (7.5 s + t)2
The green car's constant speed v would then get it to the same location in time t:
dgreen = v x t
Setting dtotal equal to dgreen and solving for v gives us the slowest constant speed the green car can maintain to catch up.