In order to qualify for the finals in a racing
event, a race car must achieve an average
speed of 230 km/h on a track with a total
length of 1810 m.
If a particular car covers the first half of the
track at an average speed of 245 km/h, what
minimum average speed must it have in the
second half of the event in order to qualify?
Answer in units of km/h
(245+r)/2 = 230 km/h
245 + r = 460
r = 460-245 = 215 km/h.
To find the minimum average speed the car must have in the second half of the event to qualify, we can use the formula for average speed:
Average speed = Total distance / Total time
First, let's calculate the time it takes for the car to cover the first half of the track. Since we know the average speed and the distance, we can use the formula:
Time = Distance / Speed
Time for the first half = (1810 m / 2) / (245 km/h) = 3.71 s
Now, let's find out how much time is left for the second half of the track. Since the total time must be the same, we subtract the time it took for the first half from the total race time:
Total time = 2 * Time for the first half = 2 * 3.71 s = 7.42 s
Since we know the total distance (1810 m) and the remaining time (7.42 s), we can use the formula for average speed to find the minimum average speed required for the second half:
Minimum average speed = Total distance / Total time = 1810 m / 7.42 s
First, we need to convert the distance from meters to kilometers:
Total distance = 1810 m / 1000 = 1.81 km
Now, let's find the minimum average speed:
Minimum average speed = 1.81 km / 7.42 s ≈ 0.244 km/s
Finally, to convert from km/s to km/h, we multiply by 3600 (since there are 3600 seconds in an hour):
Minimum average speed = 0.244 km/s * 3600 = 877.76 km/h
Therefore, the car must have a minimum average speed of approximately 877.76 km/h in the second half of the event in order to qualify.