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i have a very basic question from school days. what does it mean to say an object is moving with uniform speed? it seems to me now that it should be an unit dependent concept. for example if speed is the derivative of distance traveled, i.e. $X'(t)$ , and I decide to measure distance on a new scale $F(X)$, a monotonic function of $X$, but not a linear multiple. Then, speed in that scale at a point t would be $F'(X(t))$. $X'(t)$ , which will not be constant as $F$ can be an arbitrary increasing function.

and if indeed "uniformness of speed" is a unit dependent concept, what does it mean to say, light travels at a constant speed ? also this would mean "uniform acceleration" is also a unit dependent concept. how is then, "acceleration due to gravity" a universal constant ? would it cease to be a constant if I measured acceleration in $\log(m/s^2)$ ?

Dan
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Neat trick.

Fortunately, you're not actually changing anything physical. The graph drawn in those units would not be a straight line but the particle would still move the same distance in any fixed amount of time, i.e. it would still be uniform velocity. So it might move 8 units of distance in a 1 second interval and 16 units in the next 1 second interval but the actual distance moved would be the same in both intervals of time.

What you're doing is more like a change of coordinates than a change of units.

knucklebumpler
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