Galilean Transformation

Motion is a relative concept . You are sitting on a train. A object on trains seems to be at rest from your perspective but it is in motion from the person standing on the ground.So it is tied to particular frame of refrence choosen by observer.

Now Different observer may use different frame of refrence , And velocity ,acceleration may be different from these different frame of refrence

It is important to know how these measurement in different frame of refrence are related.

For two observer S₁ and S₂ who move relative to each other with rectilinear motion, The velocity,displacement and acceleration of an object measured from these two observer are related as

r₂=r₁ -R

Where r₁ is the position vector of object from observer S₁ and r₂ is the position vector of object from observer S₂. R is the position of observer S₂ from S₁

v₂=v₁ -v

Where v₁ is the velocity of object relative to observer S₁ and v₂ is the velocity of object relative to observer S₂. v is the velocity S₂ relative to S₁

a₂=a₁ -a

Where a₁ is the acceleration of object relative to observer S₁ and a₂ is the acceleration of object relative to observer S₂. a is the acceleration S₂ relative to S₁

When the two observer are moving in uniform relative translation motion with velocity v and t=0 when the observer were coincident,these equation becomes

r₂=r₁ -vt

v₂=v₁ -v

a₂=a₁

t₁=t₂

The above equation are called Galilean transformation of coordinates ,velocities and accelerations

So acceleration of the object remains same for all observer in uniform relative translational motion