Near the surface of Earth, acceleration is essentially constant. But while returning to Earth from the Moon, the change of distance from Earth is so great that the acceleration due to gravity changes along the way. read more
Acceleration is the rate of change of velocity (or speed) and a non constant acceleration would be the same as a varying acceleration, presumably time-varying. So having a non constant acceleration (i.e. varying) would be the same as having a rate of change of velocity that changes in time, say. read more
The average velocity expression from the constant acceleration equations works only for constant acceleration where the graph of velocity as a function of time is a straight line, the average being the midpoint of that line over the chosen time interval. read more
Example of Motion with Non-constant Acceleration The following example shows the fallibility of the formula (U_A_M 2) when applied to motion with non constant acceleration. An UFO moves at 20 m/s along a straight line for 700 m; then, suddenly it starts moving at 25 m/s along the same straight line for 600 m. read more