To qualify for the finals in a racing event, a race car must achieve an average speed of 225 km/h on a track with a total length of 1.4 km. If a particular car covers the first half of the track at an average speed of 205 km/h, what minimum average speed must it have in the second half to be able to qualify for the event?
r = 225km/h = 225000/3600s = 62.5 m/s. = Average speed for full length.
r1 = 205km/h = 205000m/3600s = 56.94 m/s.= Average speed for 1st half(700m).
(r1+r2)/2 = r
(56.94+r2)/2 = 62.5 m/s.
56.94 + r2 = 125
r2 = 125-56.94 = 68.06 m/s = Average speed for 2nd half of race.
To find out the minimum average speed the car must have in the second half to qualify for the event, we can use the concept of average speed.
Average speed is determined by dividing the total distance traveled by the total time taken. In this case, the car needs to achieve an average speed of 225 km/h over a total distance of 1.4 km.
Since we know that the first half of the track is covered at an average speed of 205 km/h, we need to determine the speed required to cover the second half of the track to meet the target average speed.
Let's assume that the second half of the track has a length of x km. Then, the first half of the track would also have a length of x km.
Using the formula for average speed, we can set up the equation:
Average Speed = Total Distance / Total Time
The total distance covered in the first half is x km, and the total distance covered in the second half is also x km. Therefore, the total distance covered is 2x km.
Average Speed = (x km + x km) / Total Time
The time taken to cover each half of the track can be calculated by dividing the distance by the speed. So the time taken for the first half is x km / 205 km/h, and the time taken for the second half is x km / Speed2.
Now, we can write the equation for the average speed:
225 km/h = (2x km) / (x km / 205 km/h + x km / Speed2)
Simplifying the equation, we get:
225 km/h = (2x km) / (x / 205 km/h + x / Speed2)
To proceed further and find the minimum average speed required, we need to solve this equation.