To qualify for the finals in a racing event a car must achieve an average speed of 250 km/h on a track with a total length of 16,000 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 to qualify
d = V*T = 16km.
250*T = 16.
T = 0.064 h. to drive the full length.
d1 = 230*t1 = 8 km.
t1 = 0.035 h to cover 1st half of the length.
t2=0.064 - 0.035 = 0.0292 h to cover the
last 8 km.
Vavg = d2/t2 = 8/0.0292 = 274 km/h.
To find the minimum average speed the car must have in the second half of the event to qualify, we need to use the concept of average speed.
Average speed is defined as the total distance covered divided by the total time taken. In this case, we are given the total distance of the track, which is 16,000 meters, and the average speed of the car for the first half of the track, which is 230 km/h. We need to determine the minimum average speed needed in the second half of the track to achieve an overall average speed of 250 km/h.
To solve this problem, we can use the formula for average speed:
Average Speed = Total Distance / Total Time
Let's calculate the time taken for the first half of the track:
Distance = Total Distance / 2 = 16,000 m / 2 = 8,000 m
Speed (in meters per second) = 230 km/h * (1000 m / 1 km) / (60 s / 1 min) / (60 min / 1 hr) = 63.89 m/s
Time = Distance / Speed = 8,000 m / 63.89 m/s ≈ 125.06 s
Now, let's calculate the time needed to achieve an average speed of 250 km/h for the entire track:
Total Time = 2 * Time
= 2 * 125.06 s = 250.12 s
To find the minimum average speed needed for the second half of the track, we need to determine how much distance must be covered in the second half:
Distance = Total Distance - Distance covered in the first half
= 16,000 m - 8,000 m = 8,000 m
Now, let's calculate the minimum average speed needed in the second half:
Speed = Distance / Time
= 8,000 m / 125.06 s
≈ 63.99 m/s
To convert this speed to kilometers per hour:
Speed = 63.99 m/s * (60 s / 1 min) * (60 min / 1 hr) * (1 km / 1000 m)
≈ 230.36 km/h
Therefore, the car must have a minimum average speed of approximately 230.36 km/h in the second half of the event to qualify for the finals.
To qualify for the finals in the racing event, the car must achieve an average speed of 250 km/h on the entire track with a total length of 16,000 m. Given that the car covers the first half of the track (8,000 m) at an average speed of 230 km/h, we can calculate the minimum average speed it must have in the second half to qualify.
To find the minimum average speed for the second half, we need to determine how much time it takes for the car to cover the first half of the track, and then calculate the remaining time available for the second half.
Time taken to cover the first half of the track:
Distance = Speed × Time
8,000 m = 230 km/h × Time
Let's convert the speed from km/h to m/s:
Speed in m/s = (230 km/h) × (1000 m/km) / (3600 s/h)
Speed in m/s ≈ 63.9 m/s
Plugging in the values:
8,000 m = (63.9 m/s) × Time
Solving for Time:
Time ≈ 8,000 m / 63.9 m/s ≈ 125.4 s
The total time available for the second half is the same as the total time for the entire track minus the time taken to cover the first half:
Total time = 2 × Time ≈ 250.8 s
To find the minimum average speed for the second half, we divide the distance remaining in the second half by the time available:
Distance remaining = Total distance - Distance covered in the first half
Distance remaining = 16,000 m - 8,000 m = 8,000 m
Minimum average speed for the second half = Distance remaining / Total time
Minimum average speed for the second half ≈ 8,000 m / 250.8 s ≈ 31.9 m/s
To convert the speed back to km/h:
Minimum average speed for the second half in km/h ≈ (31.9 m/s) × (3600 s/h) / (1000 m/km)
Minimum average speed for the second half ≈ 115.0 km/h
Therefore, the car must have a minimum average speed of approximately 115 km/h in the second half of the event to qualify for the finals.