Question

A particle moving along the circumference of a circle of radius 1m completes 3/4 of a circle in 10 second. What is the average velocity of the partcle?

Answer 1

Answer:

Average velocity = total displacement / total time taken

Total displacement of the particle = 1 - 3/4th of the circumference

⇒ (4 - 3)/4 th

⇒ 1/4 th of the circumference .

⇒ 1/4 × 2 πr

⇒ πr/2

⇒ π × 1/2

⇒ π/2

Average velocity = ( π/2 ) / (10)

⇒ π/20

The average velocity will be π/20 m/s .

Answer 2

Thus, the average velocity of the particle is π/20 m/s.

Given:

Radius = $1m$

Total displacement = $\frac{3}{4}$

Time = $10 sec$

To Find:

Average velocity.

Solution:

We know that,

Average velocity = $\frac{Total displacement}{Total time taken}$

now, the total displacement of the particle  $=(1-\frac{3}{4})$ of the circumference

we get,

$=(\frac{4-3}{4})$

$=\frac{1}{4}$ of the circumference.

Now, we get

$=\frac{1}{4}\times 2\pi r$

$=\frac{\pi r}{2}$.

$=\pi \times \frac{1}{2} \\=\frac{\pi }{2}$

now,

Average velocity $=(\frac{\pi /2}{10})$

$=\frac{\pi }{20}$

Thus, the average velocity of the particle is π/20 m/s.