Question

An athlete is running around a circular track of radius 200 m Calculate the distance and displacement
covered by athlete in-
(i) half round
(ii) one complete round (Use pie=3.14]
​

Answer 1

Let us assume that an athlete starts from point A to point B. Here it covers half of the revolution. If it return backs to its initial point i.e. A then it covers the one complete revolution.

First Case: (Half revolution)

Distance covered in one round = Circumference of circle.

{ ∴Circumference of circle = 2πr }

Given radius of circular track is 200 m.

Distance covered in half revolution = Circumstance/2

= (2 × 3.14 × 200)/2 = 628 m

Whereas, Displacement is defined as the shortest path covered between initial and starting points.

So, Displacement of the athlete = 2 × Radius of the circular track.

∴ Displacement of the athlete in half round is 400 m.

Second Case: (Complete revolution)

Distance covered = 2 × 3.14 × 200 = 1256 m

Displacement of the athlete in one complete round is zero because his/her initial and final points are same.

Answer 2

Answer:

• Half round: distance= 628 metres, displacement = 400 metres
• One round: distance = 1256 metres, displacement = 0 metres

Explanation:

Given:

Radius of the circular track = 200 metres

To find:

Distance and displacement in:

• Half round
• One complete round

Distance:

The circumference of the circle will be the distance covered in one round whereas half of the circumference will be distance covered in half roun

Half round:

Circumference of circle = $2 \pi r$

Circumference of semicircle = $\pi r$

Distance = 3.14×200

Distance = 628 metres

The distance covered in half round is equal to 628 metres

One round:

Distance = $2 \pi r$

Distance = 2×3.14×200

Distance = 1256 metres

The distance covered in one round is equal to 1256 metres

Displacement:

Half round:

The displacement at the half round will be equal to the diameter of the circle

Diameter = 2×Radius

Diameter = 2×200

Diameter = 400 metres

The displacement at end of half round will be equal to 400 metres

One round:

The displacement will be equal to 0 as the athlete will come to initial position