Question

Give an equation of motion for the height of a falling object.

Answer 1

1. An object that is falling on the surface of the earth (with an initial velocity ‘zero’) experiences acceleration due to gravity (g) in a downward direction.
2. The object reaches the ground from height (h) after the time (t), where its final velocity becomes ‘v’.
3. From the equation $S=ut+\frac{1}{2}a{t}^2$, we get

$$\begin{gathered} h=0t+\frac{1}{2}\left(g\right)t^2 \\ \Rightarrow h=\frac{1}{2}g{t}^2 \end{gathered}$$

Hence, the equation of motion for the height (h) of the object, $h=\frac{1}{2}g{t}^2$