Worked Example

Problem:
Check whether:

$$ v^2 = u^2 + 2as $$

is dimensionally correct.

Solution

Left-hand side:

$$ [v^2] = L^2 T^{-2} $$

Right-hand side:

$$ [u^2] = L^2 T^{-2} $$

$$ [2as] = LT^{-2} \cdot L = L^2 T^{-2} $$

Thus, the equation is correct.