Question

In an athletic race Bharath completed his running on a 200m circular track in 25 s and returned to the starting point.


What is the distance travelled by Bharath?


What is the displacement of Bharath?

Answer 1

Answer:

Explanation:

Given parameters

The diameter of the circular track = 200 m

Radius (r) = 200/2

r = 100 m

Time is taken by an athlete to complete one round = 40 seconds.

Displacement = ??

Speed = Distance/Time

Total time athlete moves – 2 min 20 seconds

2 min 20 seconds = 2 × 60 + 20

2 min 20 seconds = 140 seconds

Need to find the distance covered in one round

Distance covered in one round = Circumference of circle

Distance covered in one round = 2πr

Distance covered in one round = 2

Distance covered in one round = 2 × 100π

Distance covered in one round =200π

Time is taken by an athlete to complete one round = 40 seconds.

Number of rounds completed in 140s = 140/40

Number of rounds completed in 140s = 35

Distance covered = 3.5 × circumference

Distance covered = 3.5 × 2πr

Distance covered = 3.5 × 2 × 3.14 × 100

Distance covered = 2200 m

Hence, the distance covered at the end of 2 min 20 seconds is 2200 m or 22 km.

And displacement is 200 m as it returns to the initial position.

Answer 2

The diameter of the circular track is given as 200 m. That is, 2r=200 m.
From this radius is calculated as Radius, r = 100 m.
In 40 sec the athlete complete one round. So, in 2 mins and 20 secs, that is, 140 sec the athlete will complete = 140 / 40 = 3.5 (three and a half) rounds.
One round is considered as the circumference of the circular track.
The distance covered in 140 sec = 2πr×3.5=2×3.14×100×3.5=2200 m.
For each complete round the displacement is zero. Therefore for 3 complete rounds, the displacement will be zero.
At the end of his motion, the athlete will be in the diametrically opposite position. That is, displacement = diameter = 200 m.
Hence, the distance covered is 2200 m and the displacement is 200 m.