Question

A body moves in a circular track of radius 2m in 50 secs . It completes two and a half round and stops . Find the magnitude of displacement and distance covered

Answer 1

Answer:

Displacement = 2 m

Distance travelled = 15.7 m

Explanation:

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

• A body moves in a circular track of radius 2m in 50 secs.
• It completes two and a half round and stops.

We are asked to calculate the magnitude of displacement and distance covered.

Calculating displacement :

Let us say that the body starts from point A, which is its initial position.

In order to calculate the displacement, we need to find its final position. Firstly, the body covers 2 rounds, so after 2 rounds. It'll come back again to point A. Then, it covers half round which is diagrammatically opposite to point A. So, it's final position is B (refer to the attachment) which is diagrammatically opposite to point A.

Displacement is the shortest distance from initial position to final position. Here, initial position is A and final position is B. The shortest distance is always a straight line. So, AB or the diameter of the circle can be considered as the displacement.

⇒ Displacement = Diameter

⇒ Displacement = 2 m

∴ The magnitude of the displacement is 2 m.

$\rule{200}2$

Calculating distance :

⇒ Distance travelled = Distance covered in one round × (2 + ½ rounds)

• Distance covered in one round will be the perimeter of the track.

⇒ Distance travelled = ( 2πr × 2.5 ) m

⇒ Distance travelled = ( 2 × 3.14 × 1 × 2.5 ) m

• Radius is 1 m, since the diameter is 2 m.

⇒ Distance travelled = 15.7 m

∴ Distance travelled is 15.7 m.