Question

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.​

Answer 1

Given:-

Diameter of CircularTrack (D) = 200

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

200 = 2×r

r = 200/2 = 100

∴ 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 & 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.

Answer 2

Answer:

Distance covered in 1 round

= Perimeter of circular track

= 2πr (r = d/2 = 200/2 = 100)

= 2 × 3.14 × 100

= 628 m

Distance covered in 40 s = 628 m

Distance covered in 1 s = 628/40

= 15.7 m

Distance covered in 2 min 20 s or 2×60+20 or 140s

= 15.7 × 140

= 2198 m

= 2 km 198 m

Rounds covered in 40 s = 1

Rounds covered in 1 s = 1/40

Rounds covered in 140 s = 1/40 × 140 = 3.5 rounds

So,

Displacement = Diameter of track

Displacement = 200 m