In order to qualify for the finals in a racing event, a race car must achieve an average speed of 276km/h on a track with a total length of 1520m.
If a particular car covers the first half of the track at an average speed of 246km/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
7.4 waves crash onto a beach every 58.3 s.
What is their frequency?
To find the minimum average speed the car must have in the second half of the event, we can use the concept of average speed.
The formula for average speed is:
Average Speed = Total Distance / Total Time
Since we are given the first half of the track is covered at an average speed of 246 km/h, we can calculate the time taken to cover the first half of the track:
Time for first half = Distance / Speed
= 1520m / 2 / (246km/h) [since only half the track is covered]
= 1520m / (2 * 246km/h)
= 1520m / 492km/h
= 3.09 hours
Now, to qualify for the finals, the car must achieve an average speed of 276 km/h over the entire track, which is 1520m long.
For the second half of the event, we need to determine the speed required to cover the remaining distance in a specific time, so we can rearrange the formula:
Total Time = Total Distance / Average Speed
Total Time = 1520m / (276km/h)
We already know that the time taken for the first half of the track is 3.09 hours. Therefore, the time left for the second half of the track is:
Time for second half = Total Time – Time for first half
= 1520m / (276km/h) - 3.09 hours
Now, we can calculate the average speed required for the second half of the event:
Average Speed = Remaining Distance / Time for second half
Average Speed = 1520m / (1520m / (276km/h) - 3.09 hours)
Average Speed = 1520m / (1520m / 276km/h - 3.09 hours)
Average Speed = 1520m / (276km/h - 3.09 hours)
Simplifying the expression, we can convert 3.09 hours to km/h:
3.09 hours = 3.09 hours * 1/1 hour * (60 minutes/1 hour) * (60 seconds/1 minute) * (1000m/1 km) = 11124 m
So, 3.09 hours is equal to 11124 m.
Now, we can substitute the values to find the minimum average speed required for the second half of the event:
Average Speed = 1520m / (276km/h - 11124m)
Average Speed = 1520m / (276km/h - 0.011124km/h)
Average Speed = 1520m / (275.988876km/h)
Average Speed ≈ 5.51 km/h
Therefore, the car must have a minimum average speed of approximately 5.51 km/h in the second half of the event in order to qualify for the finals.