Question

Write the equation of motion for a freely falling body.

Answer 1

Hint – Discuss a freely falling body first, then move on to the general equations of motion and then substitute values in the equations according to the criteria of freely falling body so use this concept to reach the solution of the question.

Complete step-by-step solution -
Before deriving the equation of motion for a freely falling body, we must first know, what a freely falling body actually is?
A freely falling body is any object that is moving only under the influence of gravity. Such an object would experience weightlessness, similar to what you what one experiences in space. Some examples of freely falling bodies are meteors and skydivers.
General equations of motion are:
$\left( i \right)V = U + at$
$\left( {ii} \right)S = Ut + \dfrac{1}{2}a{t^2}$
$\left( {iii} \right){V^2} = {U^2} + 2as$
Where,
V = Final speed of object (time = 0),
U = Initial speed of object (time = t),
S = Distance the object covered in time t,
t = Time,
And, a = Acceleration of object.
In the case of freely falling objects, a = g (acceleration due to gravity) = $9.8\dfrac{m}{{{s^2}}}$ (considering downward direction to be positive), and u = 0. So the equations of motion now becomes:
$\left( a \right)v = u + at = 0 + gt = gt$...................... (1)
$\left( b \right)S = Ut + \dfrac{1}{2}a{t^2} = 0\left( t \right) + \dfrac{1}{2}g{t^2} = \dfrac{1}{2}g{t^2}$..................... (2)
$\left( c \right){V^2} = {U^2} + 2aS = 0 + 2aS = 2aS$.................... (3)
Equations 1, equation 2, and equation 3 are the three equations that can be used to describe the motion of any object that is in a state of free fall.
These equations are helpful in finding out variable quantities such as U, V, S and t when all the other variables are known.

Note: In reality external forces like air resistance, natural flow of wind and gravitational force applied by other celestial objects also affect the object, but, when approaching this type of theoretical questions such as the one presented here, it is better to ignore these factors, unless stated otherwise.