When a body moves in a circular path and covers a distance?

A body moves in a circle of radius 2 r what is the distance covered and displacement of body after 2 complete rounds

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CONCEPT:

Distance

• It is defined as the length of the path traveled by a body.

​Displacement

• It is the shortest distance between the initial and final position of the particle.
• It is a vector quantity.

CALCULATION:

• The distance covered along the semi-circular path is x meters.

• From the diagram, it is clear that the displacement covered along the semi-circular path will be equal to the diameter of the path.
• We know that,

⇒ x = πr     -----(1)

Where x = circumference of the semicircle and r = radius of the semicircle

By equation 1,

\(⇒ r=\frac{x}{\pi}\)     -----(2)

⇒ Displacement = 2r     -----(3)

By equation 2 and equation 3,

\(⇒ Displacement =\frac{2x}{\pi}\)     -----(4)

And,

⇒ Distance = x     -----(5)

By equation 4 and equation 5,

\(\Rightarrow \frac{Distance}{Displacement}=\frac{\pi}{2}\)

• Hence, option 1 is correct.

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A body moving along a circular path covers a distance of 3 m in 1 s uniformly, such that the body returns to its starting point.

(i) Is the body moving with uniform speed? Explain.

(ii) Is the body moving with uniform velocity? Explain

(iii) Is the motion of body along the circular path accelerated? Explain.

Please answer the question. I would be grateful... Thanks...

I can think that body is moving with uniform speed 3m/s. But fails to explain. Also body is not moving with uniform velocity as velocity is a vector quantity and body would change the direction along the circular path and thus velocity is changing every moment.

Also despite no change in speed, the body is accelerating because its direction changes all the time.

Please write in details...question wise...

I dont have enough points to comment so... a) the body is moving with uniform speed, because the object is covering a CONSTANTly increasing distance over time. And speed is directionless

b)the body is moving with a constantly changing velocity, because velocity=speed+direction, and the direction (linear) is constantly changing in a circle (tangents on the circle).

c) as an object moves in a circle, it is constantly accelerating, because objects like to move in a straight path (inertia and stuff), so to redirect that path constantly forming infinite straight line tangents on the circle, you need to apply a force to the object to turn its path. Because as newton once said, "object+force+change in position=acceleration" or something like that.