Question

an athlete runs a circular track of radius r find the distance and displacement covered by the athlete when he reaches half the circular track​

Answer 1

Explanation:

As per the provided information in the given question, we have :

• An athlete runs a circular track of radius r and covers half round.

We are asked to calculate the distance and displacement covered by the athlete when he reaches half the circular track.

Calculating distance travelled :

The athlete covers half round of the circular track. Distance convered in one round is considered as perimeter of the circular track. Since, it covers half round of the circular track. So, half of the perimeter of the circular track will be the distance travelled.

$\longmapsto \rm { Distance= \dfrac{Perimeter_{(Track)}}{2} }$

$\longmapsto \rm { Distance= \dfrac{2\pi r}{2} }$

• r = Radius

$\longmapsto \bf {Distance = \pi r }$

∴ Distance travelled is πr units.

$\rule{200}2$

Calculating displacement :

Consider the provided figure in the attachment. Suppose that the body starts from point A, which is its initial position. So, after half round, it'll come to point B, which is diagrammatically opposite to point A.

Displacement is the shortest distance from initial position to final position. So, AB or diameter of the circular track is the displacement.

⇒ Displacement = Diameter of the track

⇒ Displacement = 2 × Radius

⇒ Displacement = 2r

∴ Displacement is 2r units.