Maybe the best way to answer is what constitutes non-uniform acceleration.
Very easy example to consider is your car. Both horsepower and torque vary with RPM. So in doing a drag race scenario, you start in first gear and experience lively acceleration, the push back into the seat, the speedometer climbing rapidly, and then... the motor won't deliver. If you have a car like mine it will even cause fuel stoppage when you hit the REDline. Uniform acceleration is what technology is pushing us towards with 6 gears automatic transmissions and even beyond with continuously variable transmissions.
You feel no change from flooring it and reaching 100MPH. Its all so smooth.
Gravity is like this. Slowing your car is like this, (if you discount brake fade).
Maybe another example of non constant acceleration, kids on a merry go round pushed by friends. Every time they push a surge in speed, and overtime a buildup of speed, but not the same sensation as if we hook up motor and program it to reach the same speed without any surges ober 20 seconds.
Anytime a real thrill is involved, likely non-uniform, but to get back to usual teaching acceleration is constant. This is tremendously helpful property in lots of real world scenarios, that allow a solution to many problems and make roller coasters possible.
This help at all?