a race car must complete a 2.88-km lap if the car goes 60 m/s for the first half of the lap what must be its minimum speed for the second half to still qualify
to still qualify for the race, the average speed for the entire lap must be at least 120 m/s. Therefore, the speed for the second half of the lap must be:
average speed = total distance / total time
120 m/s = 2 * 2.88 km / (t1 + t2)
where t1 is the time taken for the first half of the lap and t2 is the time taken for the second half.
Using the formula v = d/t, we can rewrite the equation as:
120 m/s = 2 * 2.88 km / ((0.5 * 2.88 km) / 60 m/s + (0.5 * 2.88 km) / v2)
120 = 2 / ((0.5/60) + (0.5/v2))
60 = 1 / ((0.5/60) + (0.5/v2))
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
Solve for v2:
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
60 = 1 / (30 + 0.5/v2)
v2 = 120 m/s
Therefore, the minimum speed for the second half of the lap must be 120 m/s to still qualify for the race.