Relative Motion

The motion of a particle is described relative to some frame of reference, such as the ground. We can describe the motion of the same particle with respect to some other frame as well, such as with respect to a moving car.

If Position vector of particle with respect to ground

and position vector of particle with respect to ground

then Position vector of particle with respect to particle can be written as

Now velocity of particle relative to the particle is written as

Here velocity of with respect to ground
velocity of with respect to ground

Once again acceleration of particle relative to the particle is written as

where and are the acceleration of particle and with respect to ground respectively.

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