Verify that the given equation S = vᵢt + `\frac {1}{2}` at² is dimensionally correct.



Given:

S = vᵢt + `\frac {1}{2}` at²

where 
S = Distance traveled
vi = initial velocity 
t = time
a = acceleration 



To Find:

To prove that the equation S = vᵢt + `\frac {1}{2}` at² is dimensionally correct


Solution:

As given 
S = vᵢt + `\frac {1}{2}` at²  ----------(1)

We know that
Dimensions formula of S  = [L]
Dimensions formula of vi  = [LT⁻¹]
Dimensions formula of t  = [T]
Dimensions formula of a  = [LT⁻²]

Now
Dimensions formula of L.H.S. of the equation = [S] = [L]

Dimensions of R.H.S. of the equation = [vi][t] + [a][t]²
                                                        = [LT⁻¹][T]+[LT⁻²][T]²
                                                        = [L] + [L]
                                                        = 2[L]
Where 2 is an integer and dimensionless hence
                                                        = [L]
Hence proved

L.H.S = R.H.S

Hence proved that the equation S = vᵢt + `\frac {1}{2}` at²   is dimensionally correct.


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