Question

Derive v=u+at using dimension analysis.

Answer 1

SOLUTION

$let \: v \: = {u}^{m} \: + {a}^{n} {t}^{w} \\ write \: all \: the \: quantity \: in \: dimension \: form \\ \\ l {t}^{ - 1} = ( {l {t}^{ - 1} )}^{m} + {(l {t}^{ - 2} )}^{n} ( {t}^{w} ) \\ l {t}^{ - 1} = {l}^{m} {t}^{ - m} + {l}^{n} {t}^{ - 2n + w} \\ \\ compare \: powers \: we \: get \\ m = n = 1 \\ - 2n + w = - 1 \\ - 2( - 1) + w = - 1 \\ w = 1 \\ put \: these \: in \: first \: eq \\ \\ we \: get \: v = u + at$

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Answer 2

Answer:

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