Question

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

Answer 1

Answer:

Hence, we verified the L.H.S = R.H.S

Explanation:

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

s=Distance;

u= velocity;

t=Time;

a= Acceleration

Here, we have to prove L.H.S = R.H.S

Step 1:

$[s]=[ut]=[at^{2} ]$

∴ $[s]=[u]$×$[t]$

$[M^0 L^1 T^0]= [M^0 L^1 T^{-1}]$×$[T]$ $=[M^0 L^1 T^0]$

∴ LHS=RHS

Step 2:

$[s]=[at^{2} ] = [a]$ ×$[t^2]$

Therefore,

$[M^0 L^1 T^0]= [M^0 L^1 T^{-2}]$×$[T^2]$$=[M^0 L^1 T^0]$

Hence, LHS=RHS

#SPJ2