To qualify for the finals in a racing vent, a race car must achieve an average speed of 250 km/h on a track with a total length of 1,600 m. If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event in order to qualify?
find the total time needed to qualify ... 1.6 km / 250 kph
find the first half time ... 0.80 km / 230 kph
subtract to find the time needed for the 2nd half
calculate the speed necessary for the 2nd half ... 0.80 km / (time needed)
To find the minimum average speed the car must have in the second half of the event in order to qualify, we can use the formula for average speed:
Average speed = Total distance / Total time
We know that the total distance of the track is 1,600 m, and the car covers the first half of the track at an average speed of 230 km/h. Now, we need to find the total time it took the car to cover the first half of the track.
Total time = Distance / Speed
The distance covered in the first half of the track is half the total distance, so:
Distance = 1,600 m / 2 = 800 m
Speed = 230 km/h
Now we can calculate the total time:
Total time = 800 m / (230 km/h)
To convert km/h to m/s, divide the speed by 3.6:
230 km/h / 3.6 = 63.9 m/s
Total time = 800 m / 63.9 m/s ≈ 12.52 s
Since the race car must achieve an average speed of 250 km/h for the entire track to qualify for the finals, we can now find the minimum average speed the car must have in the second half.
We know that total time = time for the first half + time for the second half
Total time = 12.52 s
Time for the second half = Total time - time for the first half
Since the second half of the track is the same distance as the first half (800 m), we have:
Total time - time for the first half = 800 m / Speed for the second half
12.52 s - 800 m / 230 km/h = 800 m / Speed for the second half
Rearranging the equation to solve for the speed of the second half:
Speed for the second half = 800 m / (12.52 s - 800 m / 230 km/h)
Calculating this equation will give us the minimum average speed the car must have in the second half of the event in order to qualify for the finals.