An athlete is running on a circular track PQRS of radius 100 m shown below

He starts from point P and moves clockwise.
(i) Find the distance travelled by him and displacement when he
(a) reaches Q (b) moves from Q to S (c ) reaches P again after one revolution
(ii) If he completes one revolution in 5 minutes find his
(a) average speed (b) average velocity

Explanation

(i) (a) Total perimeter of circular tract = `2pi r=2pi(100)`m
`therefore` Distance covered `=(1)/((4)=xx2pi(100)=50pi`m
Displacement `=|(vec)(PQ)|=sqrt(PO^(2)+OQ^(2))=sqrt(r^(2)+r^(2))`
`=sqrt(2r)=100sqrt(2)m`
(b) From Q to S:
Distance covvered `=(1)/(2)xx2pir=pi r=pi r=100pi m`
Displacement `=|(vec)(QR)|=2r=200 m`
(c ) From P to P:
Distance covered `=2pi r=2xxpixx100=200pi` m
Displacement `=0` (Final position and initial position are same)
(ii) (a) Distance covered in one revolution
`2pi r=200pi m`
Time taken t=5 minutes
`therefore` Average speed `=("Distance")/("time")=(200pi)/(5"min")`
`=4pi` metre/min
Displacement in one revolution=0
(b) `therefore` Average velocity `=("Displacement")/("time")=0`