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Prove that v^2-u^2=2as using dimensional analysis?
Can you prove that v^2-u^2=2as using dimensional analysis?
Sure, let me show you. So we know that v is velocity, u is initial velocity, a is acceleration, and s is distance. Using the principle of dimensional homogeneity, we can equate the dimensions of both sides of the equation. The dimensions of v^2 are (length/time)^2, the dimensions of u^2 are also (length/time)^2, the dimensions of 2 are dimensionless, and the dimensions of a and s are (length/time^2) and length, respectively. Adding these up, we get (length/time)^2 - (length/time)^2 = (length/time^2)*length, which simplifies to (length^2/time^2) = (length^2/time^2).