If x=gt squared/2, where x is length and t is time, is dimentionally correct, ... continued in details?

Question

what are the SI units of the constant g? Thank you

Answer 1

OK, SI dimensions l, m, t (for length, mass, and time) are these: l(meter), m(kg), t(sec); so from l = x = gt^2/2 we get meter = g (sec)^2 (the 1/2 is dimensionless).

We can manipulate dimensions just like variables; so g = meter/sec^2 and that's your answer. g is an acceleration and, since g is used, it is an acceleration due to gravity forces (i.e., weight).

Another example, F = ma; where m is mass and a is acceleration, what're the force F dimensions? OK, from earlier, we have F = kg*meter/sec^2 and these are the dimensions for force. Physicists and engineers use an arcane definition for kg*meter/sec^2 and call this group of dimension Newtons.

There are other SI dimensions that could be used: l(cm), m(gm), t(sec). In which case g = cm/sec^2 is also consistent with SI dimensions. In fact, the so-called English dimensions: l(ft), m(slug), t(sec) can also be used so that g = ft/sec^2 is consistent. So in general the g dimensions are g = l/t^2 while the units used for each dimension are SI specific.

One of the most difficult parts of physics and engineering is keeping the units (dimensions) straight. In fact, for example, the trouble with the Hubble mirror some years ago was attributed to the fact that the mirror grinders used the wrong units when grinding the telescope's mirror. Physics would be a whole lot easier to learn if there were just one set of units used.

Answer 2

Correct, because unit of g is length(distance) per sq t , so you will get distance after cancelling sq t.