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 will analyze each equation step by step.

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

1. **Identify dimensions**:
- \( v_{av} \) (average velocity) has the dimension of velocity, which is \( [L T^{-1}] \).
- \( u \) (initial velocity) has the dimension of velocity, which is \( [L T^{-1}] \).
- \( v \) (final velocity) has the dimension of velocity, which is \( [L T^{-1}] \).
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