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A uniformly increasing function is linear, while a monotonically
increasing function simply increases without decreasing. A common
example of the former is uniformly accelerated motion in which
velocity increases uniformly in time. The charge on a capacitor
connected to a battery through a resistor is an example of a
monotonically increasing function of time.
I wasn't going to answer this question (I suspect everyone knew
the answer anyway), but something occurred to me. Can the motion
of a particle in a uniform gravitational field, with no other
forces applied, properly be called uniformly accelerated motion?
Leigh