Units, sig figs and dimensions

1.   This is one of the most important aspects of physics. Physicists are always particular they like to compare apples with apples and not with fruit salad.

The units of x in your equation is meters, m.

The units of u is ms-1 and time is s. When you multiply the two you get m.

The units for 'a' is ms-2 and t2 is s2 and when you multiply them you get m again.

Obviously the three terms all have the SAME units and therefore we can compare them.

2.   I always tell my students that matery of vectors and units (dimensions) is a third of the battle won with physics. You must make a serious attempt to understand how this is done so that you can even solve problems that you have no clue about just by figuring out the units and dimensions.

A simple way of representing the dimensions of something is to put it between square brackets.

[t] is read as "the dimensions of time is"

Coming to your problem

[F] = [ma]
    = [m][a]
    = [m][v/t]
    = kg[ms-1/s]

    = kgms-2 (or MLT-2)

where you've written the dimensions as MLT-2 if you represent the dimensions of mass, length and time as M, L and T.

By the same token,

    [t] = s or T
    [m] = kg or M
    [v] = ms-1 or LT-1

The dimensions of the equation on the left hand side is

[F][t] = kgms-1 or MLT-1

and the right hand side is

[m][v] = kgms-1 or MLT-1

which proves that the equation is dimensionally correct, because the dimensions or units are the same on both sides!