Question

verify S= ut + 1/2 at^2
by dimensional analysis

plz help me its urgent......!

Answer 1

S ----> displacement (L)
u ----> initial velocity ${LT}^{ - 1}$
1/2 --> no dimension
a ----> acceleration ${LT}^{ - 2}$
t ----> time (T)

substitute all the dimensional formulae according to the equation.

L = ${LT}^{ - 1}$ X T + ${LT}^{ - 2}$ X ${T}^{2}$

equating the powers of T

L = ${L}$ + ${L}$

L = 2L

2 has no dimension.

Therefore, L=L

It is dimensionally correct.