Dimensional Analysis

Dimensional analysis is a powerful tool used to:

• Verify equations
• Derive relationships
• Check consistency

Example

Consider:

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

Dimensions:

• $ut \rightarrow LT^{-1} \cdot T = L$
• $at^2 \rightarrow LT^{-2} \cdot T^2 = L$

Both terms have the dimension of length, confirming correctness.