Prove that the distances traversed during equal intervals of time by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity [namely 1: 3: 5: …………….].

Explanation

To prove that the distances traversed during equal intervals of time by a body falling from rest stand to one another in the same ratio as the odd numbers beginning with unity (1: 3: 5: ...), we can follow these steps:

### Step 1: Understanding the Problem
We need to find the distances traveled by a body falling freely under gravity during equal time intervals. The body starts from rest, so the initial velocity \( u = 0 \).

### Step 2: Using the Equation of Motion
For a body falling freely under gravity, the distance traveled in \( n \) seconds can be calculated using the equation:
\[
...