Question

An athlete completes one round of a circular track of diameter 200 m in
40 s. If he continues to run, what will be the distance covered and the
displacement at the end of 2 minutes 20 s respectively?

Answer 1

Explanation:

☞Answer:-

Given:-

• circular track of the diameter is 200 m in 40 s.

To find:-

• displacement at the end of 2 minutes 20 s respectivel.

Solution:-

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

Explanation:

Given that the diameter of the circular track is 200 m. So, radius (r) = 200/2 = 100 m

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

Now,

Speed = Distance/Time

Total time athlete moves is 2 min 20 seconds

2 min 20 seconds = 2 × 60 + 20 = 120 + 20 = 140 seconds

Distance covered in one round = Circumference of a circle

Distance covered in one round = 2πr

= 2 × 100 × π

= 200 π

Also, the tme is taken by an athlete to complete one round = 40 seconds.

Number of rounds completed in 140 seconds = 140/40 = 3.5

Distance covered = Number of rounds completed in 140 seconds × circumference

= 3.5 × 2πr

= 3.5 × 2 × 22/7 × 100

= 2200 m

Displacement of an athlete in 2 minutes will be zero because the he will complete 3 rounds and at that time initial and final positions will be same. In later 20 seconds the displacement will be equal to the diameter of the circular track i.e. 200 m.

Displacement = diameter = 200 m

Therefore, the distance covered at the end of 2 min 20 seconds is 2200 m and displacement is 200 m.