Question

Dimensional equations S=ut+1/2at^2 prove that...
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Answer 1

Given :

• Dimensional equation : S = ut + 1/2 at²

To prove :

• This equation is dimensionally correct .

Proof :

• For any equation to be dimensionally correct , all the terms of the equation should have the same dimensional formula.
• This equation contains three terms : s , ut and 1/2 at² .
• For this equation to be correct , all three terms should have same dimensions. Let us check .

TERM 1 :

s : Here 's' is a term for displacement which is length . The dimension of length is given by [L] .

Therefore , s = [L]

TERM 2 :

ut : Here 'u' is velocity and t is time . The dimensional formula of u is $\tt [LT^{-1}]$ and t is [T] .

$\therefore \tt ut = [LT^{-1}][T]$

ut = [L]

TERM 3 :

1/2 at² : 1/2 is a numerical value and has no dimension. Here 'a' is acceleration with dimensional formula $\tt [LT^{-2}]$ and 't' is time with dimensional formula [T] .

$\therefore \tt \dfrac{1}{2} at^2 = [LT^{-2}][T^2]$

1/2 at² = [L]

Since the dimensions of each term is coming out to be similar to other terms , this equation is dimensionally correct .