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

Solution:

Diameter of a circular track (d)= 200 m

Radius of a circular track (r)= d/2=200/2=100 m

Time taken to complete one round= 40 s

Total time taken= 2 min 20 sec
= 2× 60+ 20= 120+20=140sec

[ 1 min= 60sec]

Length of a circular track(circumference) = 2πr
= 2× 22/7 × 100= 4400/7m

Distance travel in 40 seconds= 4400/7 m

Distance travelled in 140 seconds=
(4400/7) × 140/40= 2200 m

To find the displacement of the athlete we have to find his position on the track at the end of 2 minutes and 20 sec.

We have to find the number of rounds completed in the distance of 2200 m.

Number of rounds in 2200 m= total distance/ circumference
=2200× 7/4400= 3.5

Since in one complete rotation the displacement is zero as an athlete reaches the same position, therefore the displacement in 3.5 rounds will be equal to the diameter of the track as the athlete will be totally opposite to the starting point. i.e

Displacement= diameter of the track= 200 m .

Hence the distance travelled at the end of 2 minute 20 second is 2200 m and the displacement is 200m.

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Hope this will help you.....

Answer 2

At the end of 2 minute 20 seconds the distance covered is 2198 m and displacement is 200m.