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?
traight​

Answer 1

Correct Question

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An athlete completes one round of a circular track of diameter 200m in 40s.

What will be the distance covered and the displacement at the end 2 min 20s

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⇨Diameter of the Circular Track = 200 m

Therefore, Calculating Radius = D/2 = 200/2 = 100m

⇨Time taken for Completing one round = 40 s

⇨Time taken to come at final point = 2 min 20 sec = (2 × 60 + 20)sec = 140 sec

⇨Number of Round Completed = 140/40 = 3.5

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We Have to Find:-

• Distance Covered
• Displacement Covered

Finding Distance Covered

➯ (2πr)(3.5)

➯ $\tt (2 \times \dfrac{22}{7} \times 100)(3.5)$

➯ $\tt 2 \times \dfrac{22}{ \cancel{7}} \times 10 \cancel{0} \times \dfrac { \cancel{35}}{1 \cancel{0} }$

➯ $\tt 2 \times 22 \times 10 \times 5$

➯ 2220 m or 2.2 km

Finding Displacement Covered

Noow, rounds in 140 s = 140/40= 3.5 rounds

Displacement is zero, as it is Circular Track

If he covers three rounds, Displacement will still be zero

Displacement for 0.5 (1/2) round= Diameter of Circular track =200m

Thus,

Distance = 2200 m

Displacement = 200 m

Answer 2

Given:-

• Diameter of CircularTrack (D) = 200

D = 2r (where r is the radius of circular track)

200 = 2×r

r =200/2

r = 100 m

∴ Radius of the circular track = 100 m.

• Time taken by athlete to complete on round of square circular track = 40 s

• Total time taken by athlete = 2 min 20s= 2 ×60 + 20 = 140 s (here min is convert into second).

To Find :-

• Distance and Displacement at the end of 2 min 20 s.

Solution:-

According to the Given Question

Distance covered by athlete in one round on circular track = 2πr

Putting all the values which is given above

⟹ 2 × 22/7 × 100

⟹ 4400/7

We know that ,

Speed = Distance/Time

⟹ S = 4400/7×40

⟹ S = 4400/280

Now,

Distance covered by athlete in 140 s = Speed × Time.

⟹ Distance = 4400 × 140/280

⟹ Distance = 4400/2

⟹ Distance = 2200 m

or,

2200/1000= 2.2 Km.

∴ The distance covered by athlete at the end of 140s = 2.2 km.

And, we have to calculate the Displacement . So,

Displacement is the shortest path between two points.

No. of round in 40s = 1 Round

No. of rounds in 140 s = 140/40= 3.5 rounds

If athletes cover one round then there displacement is Zero

Similarly if he covers 3 round then there displacement is zero.

Now, Displacement for 0.5 (1/2) round= Diameter of Circular track =200m

∴ The displacement of athlete after 140 s

is 200 m.