v^2=u^2 +k*s, what is the dimension of k?

Question

anonymous · Answer

If we rearrange the formula we get $$\frac{v^2-u^2}{s}=\frac{V^2}{s}=k$$ where the $V^2$ represents the difference in the square of the velocities (as we are only interested in units, and this helps avoid some confusion later). Now we can plug in the units just as if we were putting in numbers to solve it.  For example if v = 2 m/s then we just put in m/s and don't worry about the 2.

so plugging in the units we get $$\frac{(m/s)^2}{m}=\frac{m^2}{ms^2}=\frac{m}{s^2}=k$$So teh units for k are metres per square second (m/s$^{2}$), which are the unites of acceleration.  Which is good, as we know that the full equation should be $v^2=u^2+2as$, so we have confirmed the equation.

anonymous · Answer

I just seen that the question asks for dimensions, not units.  thtas no problem.  instead of puting units in, substitute L for m and T for s, in the above, where L stands for Length, and T for Time.  you will then obtain an answer of $$\frac{L}{T^2}$$  This is commonly expressed as $LT^{-2}$