A quick way to sanity-check a set of motion equations without re-deriving them is to test whether every term in each equation has matching physical dimensions, since a dimensionally inconsistent equation could never be physically valid.
Step 1: For \( v = u + at \): \( v \) and \( u \) are velocities with dimension \( [LT^{-1}] \). The term \( at \) has dimension \( [LT^{-2}][T] = [LT^{-1}] \). All terms match, so the equation is dimensionally sound.
Step 2: For \( s = ut + \frac{1}{2}at^2 \): \( s \) has dimension \( [L] \). The term \( ut \) gives \( [LT^{-1}][T] = [L] \), and \( at^2 \) gives \( [LT^{-2}][T^2] = [L] \). Every term matches \( [L] \), so this equation is also dimensionally sound.
Step 3: For \( v^2 = u^2 + 2as \): both sides have dimension \( [L^2T^{-2}] \), since \( as \) gives \( [LT^{-2}][L] = [L^2T^{-2}] \). This equation checks out as well.
Since all three equations pass the dimensional consistency test, none of them can be rejected as invalid, so the correct choice must include all of them: \[ \boxed{\text{all of these}} \]