Introduction:
The Galilean transformation is a set of equations that relate the space and time coordinates of an event as observed in one inertial reference frame to the coordinates of the same event as observed in another inertial reference frame. In this context, we want to show that acceleration is invariant under Galilean transformation.

Galilean Transformation:
The Galilean transformation equations are given by:
- x' = x - vt
- y' = y
- z' = z
- t' = t

Definition of Acceleration:
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it is given by:
- a = dv/dt

Proof:
To show that acceleration is invariant under Galilean transformation, we need to demonstrate that the value of acceleration remains the same in both reference frames.

Step 1: Velocity Transformation
Using the Galilean transformation equations, we can express the velocity in the primed frame (v') in terms of the velocity in the unprimed frame (v):
- v' = v - u

Step 2: Differentiation of Velocity Transformation
Differentiating the velocity transformation equation with respect to time, we get:
- a' = dv'/dt = dv/dt - du/dt

Step 3: Invariance of Acceleration
Now, let's consider the acceleration in the unprimed frame (a). Since acceleration is the rate of change of velocity with respect to time, we can write:
- a = dv/dt

Step 4: Final Comparison
Comparing the expressions for a' and a, we have:
- a' = a - du/dt

Conclusion:
From the above comparison, we can conclude that the acceleration in the primed frame (a') is equal to the acceleration in the unprimed frame (a) minus the rate of change of the relative velocity between the two frames (du/dt). Therefore, acceleration is invariant under Galilean transformation.