Which one of the following equations related to the motion of an...

The standard equations of motion for an object moving with constant acceleration are:

$v = u + at \Rightarrow u = v - at$

$s = ut + \dfrac{1}{2}at^2$

$v^2 - u^2 = 2as$

$S_n = u + \dfrac{1}{2}a(2n-1)$

Comparing these with the given options:

Option (1) matches the second equation of motion.

Option (2) is a valid rearrangement of the first equation of motion.

Option (3) is given as $u^2 - v^2 = 2as$, which contradicts the third equation of motion $v^2 - u^2 = 2as$. Thus, it is incorrect.

Option (4) correctly gives the displacement in the $n^{th}$ second.

Therefore, the incorrect equation is $u^2 - v^2 = 2as$.