Question

How is the distance related with time for the motion under uniform acceleration such as the motion of a freely falling body starting from rest?

• A. $S\propto t^2$
• B. $S\propto t$
• C. $S\propto \frac{1}{t^2}$
• D. $S\propto \frac{1}{t}$

Answer 1

The correct option is A $S\propto t^2$

For a free falling body, initial velocity, $u=0m/s$ and acceleration due to gravity, $a=g$.
Putting the values of $u$ and $a$ in the equation of motion, $S=ut+\frac{1}{2}a{t}^2$
We get, $S=\frac{1}{2}g{t}^2$
Therefore, $S\propto t^2$