Question

a particle is moving with constant speed v on a circular path of radius r when it has moved by angle 60 find displacement and average velocity and average acceleration​

Answer 1

Answer:

According to the problem the speed of the  particle is v

the radius of the circular path is r

Now the particle has moved 60 °

Follow the diagram,

we can find that there is an equilateral triangle having equal side length. therefore the displacement,d is equal to the radius of the circle.

We know that the average velocity of any particle can be found by

Average velocity of the particle is = total displacement / time

As the radius of the circle is r

and  Displacement,d  =  r

Now,  the total time taken by the particle to cover the circular path is or to cover 360°

Let t is the needed time

t= 2 π r /v

Therefore time taken to cover  60 °

⇒ t 1 = 1 /6T

Tt1 = π r /3 v

So, average velocity  = r /π r /v

= v /π

Now to find the average acceleration,a = change in velocity / time

According to the diagram the particle started with its velocity pointing upwards and after moving 60 ° it made the angle vertically

let the change in the velocity,

Let ultimate velocity be v 2  and starting velocity v1

Therefore change in velocity

Δ V = √ ( v 1^2+ v2^2-2v1v2cos60 °)

According tot he problem the particle didn't change its velocity

therefore v 1=v2

hence

Δ V = v 1

   = v

Therefore the average acceleration,a : v/π r /3 v

                                                            = 3v^2/π r