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` ?

Answer

(a) distance =2200 m ; displacement=200 m.

Explanation

Diameter of circular track (D) = 200 m
Radius of circular track (r ) = 200/2 = 100 m
Time taken by the athlete for one round (t) = 40s
Distance covered by athlete in one round (S) = `2pir`
= `2xx(22//7)xx100`
speed of the athlete (v) = Distance /Time
= `(2xx2200)//(7xx40)`
= 4400/ 7`xx`40
Therefore, Distance covered in 140 s = Speed (s) `xx` Time (t)
`= 4400//(7xx40)xx(2xx60+20)`
`=4400//(7xx40)xx140`
`=4400xx140//7xx40`
= 2200 m
Number of round in 40 s = 1 round
Number of round in 140 s = 140/40
`=3^(1//2)`
After taking start from position X, the athlete will be at postion Y after `3^(1//2)` rounds as shown in figure.

Hence, Displacement of the athlete will respect to initial position at x = xy
= Diameter of circular track
= 200 m