A cyclist is participating in a 5 km race by cycling along the perimeter of a circular track of radius 35 m He increases his speed by 4 m/s after each round If he started cycling at 4 m/s what is his average speed for the last 440 m?
Answers
Given : A cyclist is participating in a 5 km race by cycling along the perimeter of a circular track of radius 35 m He increases his speed by 4 m/s after each round
To find : what is his average speed for the last 440 m
Solution:
perimeter of a circular track of radius 35 m = 2 π * 35
= 2 ( 22/7) * 35
= 220 m
Total Race = 5 km = 5000
Total Round = 5000/220 = 22.7
Last round 23 rd is only 5000 - 22(220) = 160 m
22nd round = 220 m
21st round = 440 - 220 - 160 = 60 m
Speed in 1st round = 4 m/s
then speed increased in each round by 4 m/s
Speed in 21st round = 4 + 20 * 4 = 84 m/s
Speed in 22nd round = 88 m/s
Speed in 23rdround = 92 m/s
Time = Distance / Speed
Total time taken for last 440 m = 60/84 + 220/88 + 160/92
= ( 5/7 + 5/2 + 40/23)
= ( 230 + 805 + 560 )/322
= 1595 / 322
Average Speed = 440 / ( 1595 / 322 ) = 88.83 m/s
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