1) To find the average velocity of the bus, we first need to know the displacement and the time taken. In this case, the displacement is the distance between your home and school, which is 10.0 km. The time taken is given as 0.53 hours.
Average velocity is calculated by dividing the displacement by the time taken:
Average velocity = displacement / time taken
Plugging in the values, we get:
Average velocity = 10.0 km / 0.53 h
To simplify this calculation, we convert the time from hours to seconds:
Average velocity = 10.0 km / (0.53 h * 3600 s/h)
Now we can convert the distance from kilometers to meters:
Average velocity = (10.0 km * 1000 m/km) / (0.53 h * 3600 s/h)
Simplifying, we find:
Average velocity = 5.917 m/s
Therefore, the average velocity of the bus is 5.917 m/s.
2) To calculate the minimum average speed required in the second half of the event, we need to find the remaining distance the car needs to cover and the time it has to do so.
The total length of the track is given as 1600m, and the first half is covered at an average speed of 230 km/h. Therefore, the distance covered in the first half of the event is 800m.
To find the remaining distance, we subtract the distance covered in the first half from the total length of the track:
Remaining distance = 1600m - 800m
= 800m
Now we need to know the time available to cover the remaining distance. For this, we need to know the average speed of the car in the first half.
Average speed is calculated by dividing the total distance covered by the time taken:
Average speed = distance covered / time taken
Since the distance covered in the first half is 800m and the average speed is given as 230 km/h, we can calculate the time taken as:
Time taken = distance covered / average speed
Time taken = 800m / (230 km/h * 1000 m/km/ 3600 s/h)
Simplifying, we find:
Time taken = 0.124 s
Therefore, the car has 0.124 seconds to cover the remaining 800m in the second half of the event.
Now we can find the minimum average speed required in the second half. The remaining distance is 800m, and the time available is 0.124 seconds.
Average speed = distance / time
Average speed = 800m / (0.124 s)
Simplifying, we find:
Average speed = 6451.6 m/s
Therefore, the car must have a minimum average speed of 6451.6 m/s in the second half of the event to qualify for the finals.