# Mechanics: Chapter 11 – Relative Velocity and Acceleration

If two reference frames A and B are different from each other only because they are moving at different constant velocities relative to each other, we can convert the displacements, velocities and accelerations with respect to A to the displacements, velocities and accelerations with respect to B using Galilean Transformation.

If at time $t = 0$, the origins of both A and B coincide, and B is moving at a constant velocity $v_{0}$ with respect to A, then the displacement with respect to B, $r_{B}$ can be calculated from the displacement with respect to A, $r_{A}$ at time $t$ using:

• $r_{B} = r_{A} - v_{0}t$

Differentiating this with respect to time, we get,

• $v_{B} = v_{A} - v_{0}$

and taking the second derivative, we get

• $a_{B} = a_{A}$

Interestingly, acceleration remains the same in reference frames that can be transformed using Galilean transformation.