   Chapter 2, Problem 15P

Chapter
Section
Textbook Problem

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 1.60 × 103. 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?

To determine
The average speed of the car in the second half of the race.

Explanation

Given Info:

The average speed of car is 250km/h .

The average speed of car in first half of the race is 230km/h .

The total distance covered is 1.60×103km .

Explanation:

The formula used to calculate the time taken by the car to cover the total distance is,

t=xv¯

• t is the time taken to complete the race
• x is the distance covered in the race
• v¯ is the average velocity of the car

The formula used to calculate the time taken by the car to cover the first half of the total distance is,

t1=(x/2)v¯1

• t1 is the time taken to complete the first half of the race
• v¯1 is the average velocity of the car in the first half of the race.

The formula used to calculate the time taken by the car to cover the second half of the total distance is,

t2=tt1

• t2 is the time taken by the car to complete second half of the race

Substitute x/v¯ for t and (x/2)/v1¯ for t1 to find t2 .

t2=xv¯x/2v1¯

The formula used to calculate the average velocity of the car in second half of the race is,

v¯2=(x/2)t2

• v¯2 is the average velocity of the car in second half of the race

Substitute xv¯x/2v¯1 for t2 to find v¯2

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