5.0 Vertical motion under gravity

  Motion in One Dimension

When a body is thrown vertically upwards or dropped from a height, it moves in a vertical straight line is an example of motion in one dimension.

If the air resistance offered by air to the motion of the body is neglected, all bodies fall freely under gravity.

The acceleration produced by the gravity is known as acceleration due to gravity.

It is represented by $g$.

Value of $g$ is $9.8\,m/{s^2}$ or $10\,m/{s^2}$.

Since the acceleration due to gravity is constant. So, all the kinematics equation is constant.
$$\overrightarrow v = \overrightarrow u + \overrightarrow a t$$$$\overrightarrow s = \overrightarrow u t + \frac{1}{2}\overrightarrow a {t^2}$$$${v^2} = {u^2} + 2\overrightarrow a .\overrightarrow s $$

where,

$\overrightarrow a = - g$

Note: As $\overrightarrow v $, $\overrightarrow u $ and $\overrightarrow a $ are all vector quantities. So, proper sign convention should be always followed.