Question

An athlete completes 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 1

Answer:-

Distance covered = 2200 m

Displacement = 200 m

Given:-

Diameter of track  = 200 m

Radius of track  = $\frac{200}{2}$ = 100 m

Time taken by the athlete to cover 1 round  = 40 s

Explanation:-

Distance covered by athlete in one round = 2πr

⇒ 2 × ( $\frac{22}{7}$ ) × 100

Speed of the athlete = $\frac{Distance}{Time}$

⇒ (2 × 2200) / (7 × 40)

⇒ 4400 / 7 × 40

So, Distance covered in 140 s = Speed × Time

⇒ 4400 / (7 x 40) x (2 x 60 + 20)

⇒ 4400 / ( 7 x 40) x 140

⇒ 4400 x 140 /7 x 40

⇒ 2200 m

No. of rounds in 140 s

= $\frac{140}{40}$

= 3$\frac{1}{2}$

At the end of his motion, the athlete will be in the diametrically opposite position.

Or, displacement = diameter = 200 m

Answer 2

Ans:

Time taken = 2 min 20 sec = 140 sec.

Radius, r = 100 m.

InTime to complete one round = 40 sec

So, Round completed in 140 sec

= 140 ÷ 40 = 3.5 (three and a half) round.

distance covered = 2 x 22/7 x 100 x 3.5

= 2200 m.

At the end, the athlete cavers half round and will be at a distance

= diameter of circle. ie displacement

= 200m.