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An athlete complete one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s ?

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Answer Text

Answer :
(a) distance =2200 m ; displacement=200 m.
Solution :
Diameter of circular track (D) = 200 m <br> Radius of circular track (r ) = 200/2 = 100 m <br> Time taken by the athlete for one round (t) = 40s <br> Distance covered by athlete in one round (S) = `2pir` <br> = `2xx(22//7)xx100` <br> speed of the athlete (v) = Distance /Time <br> = `(2xx2200)//(7xx40)` <br> = 4400/ 7`xx`40 <br> Therefore, Distance covered in 140 s = Speed (s) `xx` Time (t) <br> `= 4400//(7xx40)xx(2xx60+20)` <br> `=4400//(7xx40)xx140` <br> `=4400xx140//7xx40` <br> = 2200 m <br> Number of round in 40 s = 1 round <br> Number of round in 140 s = 140/40 <br> `=3^(1//2)` <br> After taking start from position X, the athlete will be at postion Y after `3^(1//2)` rounds as shown in figure. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_SCI_IX_C08_E01_028_S01.png" width="80%"> <br> Hence, Displacement of the athlete will respect to initial position at x = xy <br> = Diameter of circular track <br> = 200 m

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