Question

Consider two cyclists (Mike and Adam) racing on course of length d. Mike travels the complete racetrack at an average speed of v. Adam covers the first half of the course length at speed v/2, then covers the second half at speed 2v. a) Who wins the race? b) Where is the loser when the winner crosses the finish line?

Answer 1

a) Mike wins the race

b) 0.5d

Step-by-step explanation:

Mike's kinematics :

t₁ = d/v : time spent Mike to reach the finish line

Adam's kinematics :

`t_(2) = ((d)/(2) )/((v)/(2) ) +((d)/(2) )/(2v)`

`t_(2) = (d)/(v) + (d)/(4v)`

t₂= 1.25 d/v : time spent Adam to reach the finish line

a) Mike wins the race because he spends less time .

t₁ < t₂

b) We calculate the time difference to determine the distance Adam is from the finish line

t₂-t₁ = 1.25 d/v- d/v

t₂-t₁ = 0.25 d/v

x=2v*0.25 d/v

x= 0.5d : Adam's distance to reach the finish lin