Reference frame in relative motion

[manimaran1605]

I red a classical mechanics concept in a book. Imagine that we have two observers with two frames of reference F1 and F2 observing a particle P in motion. One of the observer is in motion and another is at rest,(lets take F1 is at rest and F2 is in translation motion with velocity V) let r1 be the position vector of particle with relative to frame of reference F1 and r2 be the position vector of particle with relative to frame of reference r2, the relation between r1 and r2 be r1-D=r2 ( D be the postion vector of F2 relative to F1), to find it velocity at any time t we differentiate r1 with respect to 't', we get v=V+(dr2/dt)F1 where v is the velocity of the particle relative to the frame of reference F1, V is the velocity of the F2 relative to F in straight line, (dr2/dt)F1 is the velocity of the particle relative to F1, How? in the book it is also taken that velocity of particle relative to F1 is taken equal to velocity of particle relative to F2 and said velocity of the particle is equal to the sum of velocity of particle relative to F2 and velocity of frame F2, How can we assume the velocity of particle relative to F1 is taken equal to velocity of particle relative to F2?

 

[Simon Bridge]

I red a classical mechanics concept in a book.

Which book - citations are important.

Imagine that we have two observers with two frames of reference F1 and F2 observing a particle P in motion.

Is this particle in motion with respect to both F1 and F2?

One of the observer is in motion and another is at rest, (lets take F1 is at rest and F2 is in translation motion with velocity V) let r1 be the position vector of particle with relative to frame of reference F1 and r2 be the position vector of particle with relative to frame of reference r2, the relation between r1 and r2 be r1-D=r2 ( D be the postion vector of F2 relative to F1),

... when D=0, the origin's coincide.

to find it velocity at any time t we differentiate r1 with respect to 't', we get v=V+(dr2/dt)F1 where v is the velocity of the particle relative to the frame of reference F1,

What is F1 "stationary" with respect to then?
I have a feeling this is the crux of the matter for you.

V is the velocity of the F2 relative to F in straight line, (dr2/dt)F1 is the velocity of the particle relative to F1,

If r1 is the displacement of the particle in F1, then v=dr1/dt would be the velocity of the particle in F1. dr2/dt would be the velocity of the particle in F2. The notation "(dr2/dt)F1" needs to be clarified.

How? in the book it is also taken that velocity of particle relative to F1 is taken equal to velocity of particle relative to F2 and said velocity of the particle is equal to the sum of velocity of particle relative to F2 and velocity of frame F2, How can we assume the velocity of particle relative to F1 is taken equal to velocity of particle relative to F2?

You can't. Either the book is talking rubbish or you have misunderstood something.