An object acceleraties uniformly from initial velocity u to final velocity v. if travels distance s in time t. Then check the dimensional consistency of the following equations. Which of them are correct physically?
(i) `v_(av)=(u+v)/3`
(ii) `s=ut+1/2at^(2)`
(iii) `v^(2)-u^(2)=(2s)/a`

Explanation

To check the dimensional consistency of the given equations, we need to ensure that the dimensions on both sides of each equation are equal. Let's analyze each equation step by step.

### Given Equations:
1. \( v_{av} = \frac{u + v}{3} \)
2. \( s = ut + \frac{1}{2}at^2 \)
3. \( v^2 - u^2 = \frac{2s}{a} \)

### Step 1: Check the first equation \( v_{av} = \frac{u + v}{3} \)
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