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 , the origins of both A and B coincide, and B is moving at a constant velocity with respect to A, then the displacement with respect to B, can be calculated from the displacement with respect to A, at time using:
Differentiating this with respect to time, we get,
and taking the second derivative, we get
Interestingly, acceleration remains the same in reference frames that can be transformed using Galilean transformation.