Race: Blythe and Geoff compete in a 1-km race. Blythe’s strategy is to run the first 600 m of the race at a constant speed of 4 mm/ss, and then accelerate with constant acceleration to her maximum speed of 7.5 mm/ss, which takes her 1 min, and finish the race at that speed. Geoff decides to accelerate with constant acceleration to his maximum speed of 8 m/s at the start of the race and to maintain that speed throughout the rest of the race. It takes Geoff 3 min to reach his maximum speed. Who wins the race?

From the value of each person's time to finish the race, it can be concluded that Geoff will win the race.

Explanation:

Given;

total distance to be covered, d = 1000 m

first distance covered by Blythe, = 600 m

constant speed of Blythe at the first stage, = 4 m/s

final speed of Blythe, = 7.5 m/s

time of Blythe's constant acceleration, = 1 min = 60 s

initial speed of Geoff, = 0

final speed of Geoff, = 8 m/s

time of Blythe's constant acceleration, = 3 min = 180 s

The acceleration of Blythe is given as;

distance covered by Blythe during this acceleration is given as;

The remaining distance covered by 7.5 m/s is given as;

The total time for Blythe to covere the entire distance = time taken to cover 600 m + time taken to cover 344.94 m + time taken to cover 55.06 m

The acceleration of Geoff  is given as;

distance covered by Geoff during this acceleration is given as;

The remaining distance covered by 8 m/s is given a;

The total time for Geoff to covere the entire distance = time taken to cover 712.8 m + time taken to cover 287.2 m

Therefore, from the value of each person's time to finish the race, it can be concluded that Geoff will win the race

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