Question

To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/hr on a track with a total length of 1600 m. If a particular car covers the first half of the track at an average speed of 225 km/hr, what minimum average speed must it have in the second half of the event in order to qualify?

Answer 1

Answer on Question #61895, Physics / Classical Mechanics

To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/hr on a track with a total length of 1600 m. If a particular car covers the first half of the track at an average speed of 225 km/hr, what minimum average speed must it have in the second half of the event in order to qualify?

Solution:

The time that car can spend on the whole race is total length divided by total average speed:

$$\frac{1.6}{250} = \frac{4}{625} \text{ hours}$$

The time that car spend on the first half of the race is half length divided by average speed on that part:

$$\frac{0.8}{225} = \frac{4}{1125} \text{ hours}$$

The time left is

$$\frac{4}{625} - \frac{4}{1125} = \frac{16}{5625} \text{ hours}$$

The average speed for the second part of the race is half length divided by remaining time:

$$\frac{0.8}{\frac{16}{5625}} = 281.25 \text{ km/hr}$$

Answer: 281.25 km/hr is the minimum average speed for the second part of the race.

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