Final answer:
The equation v² = u² + 2as is dimensionally consistent as each term has the dimension L²T⁻². Dimensional analysis confirms the potential plausibility of equations in physics, though it doesn't ensure numerical accuracy.
Step-by-step explanation:
Checking the correctness of equations dimensionally is essential in physics to ensure they represent possible physical relationships. The given equation v² = u² + 2as is to be checked for dimensional consistency. First, analyze the dimensions of each term:
- The dimension of v² (velocity squared) is (LT⁻¹)² = L²T⁻².
- The dimension of u² (initial velocity squared) is also L²T⁻².
- For 2as, 2 is a dimensionless constant, [a] is acceleration with a dimension of LT⁻², and [s] is displacement with a dimension of L, so its dimension is L(LT⁻²) = L²T⁻².
Seeing that all terms have the same dimension of L²T⁻², we conclude that the equation v² = u² + 2as is dimensionally consistent.
Dimensional analysis not only helps to check for algebraic mistakes but also serves as a quick tool to confirm the plausibility of physical equations. However, it is essential to remember that dimensional consistency doesn't guarantee the numerical correctness of an equation.