Question

the distance travelled by a body falling from rest in one two and three second are in the ratio ​

Answer 1

This one is pretty straight forward question!!

Here Galileo 's law of odd numbers applies:

The Galileo’s law of odd numbers states that the distances traveled are proportional to the squares of the elapsed times. In other words, in equal successive periods of time, the distances traveled by a free-falling body are proportional to the succession of odd numbers(1,3,5,7, etc.).

In simple language.....

The ratio will be 1:3:5

Now, if you don't feel this.......

you can use the kinematic equations:

The distance travelled is given by

$s = 1 \ \div 2 \: \: \times g {t}^{2}$

With these.... you can plug in the values of seconds in the time and get the required ratio!!

Or if you can memorize a single formula for this one..

$s = u + 0.5 \times a(2n - 1)$

This formula can be used to calculate the displacement in the nth seconds!

Hope that you find any of these methods useful and efficient in your journey to success!

Thanks :)