Problem 64.

To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 2000 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?

Solution:

The average speed is the ratio of traveled distance and traveled time:

For the whole track we have: and . Then the traveled time is

The car travels the first half of the track (1 km) with speed 230 km/h. The time of this motion is

Since the total traveled time should be 0.008 h, then the second part of the track the car should travel 0.008-0.0043 = 0.0037 h. Since the distance of this motion is 1 km, then the average speed is