Question

Can there be displacement of an object in the absence of any force acting on it?

Answer 1

Here in this question we have to know whether there would be any displacement of an object and for this we will use the velocity relation and is given by $v = \dfrac{s}{t}$ . So by using the second equation of motion which is given by $s = ut + \dfrac{1}{2}a{t^2}$ , we will be able to know the answer.

Complete step by step answer:
Displacement: The change of position. In other words the distance travelled by an object.
Velocity: The velocity of an object is defined as the change of rate of its position with respect to time and direction i.e. velocity is the rate of change of displacement with respect to time.
Velocity,
$v = \dfrac{s}{t}$
Where,
$v$ , is velocity.
$s$ , is displacement.
$t$ , is time.
The newton’s first law of motion states that the object remains to be in rest or uniform motion unless it is affected by the external force.
So, if an object is moving with a constant velocity then there can be displacement where force has no place to affect the object’s displacement.
We can use the equation of motion to prove that there can be displacement of an object even in the absence of any force acting on it.
There are three equations of motion. It is used to derive components such as displacement, velocity, time and acceleration.
First Equation of Motion, $v = u + at$
Second Equation of Motion, $s = ut + \dfrac{1}{2}a{t^2}$
Third Equation of Motion, ${v^2} = {u^2} + 2as$
Where,
$u$ , is the initial velocity.
$v$ , is the final velocity.
$a$ , is the acceleration.
$t$ , is the time period.
$s$ , is the distance travelled i.e. displacement.
From the second equation we can calculate the displacement.
Second Equation of Motion, $s = ut + \dfrac{1}{2}a{t^2}$
Here there is no acceleration.
If an object has a constant velocity then it has zero acceleration because acceleration is the change in velocity since there is no change in velocity there is no acceleration. There is no net force acting on the object as force is defined as the product of mass and acceleration. There is no acceleration so there is no force.
Then the equation becomes
Second Equation of Motion, $s = ut + \dfrac{1}{2}a{t^2}$
$\Rightarrow s = ut + 0$
And on solving it, we get
$\Rightarrow s = ut$
The object has a constant velocity $u$ in time $t$ .
Hence, if an object is moving with a constant velocity then there can be displacement where force has no place to affect the object’s displacement.
So, the answer is yes, there can be displacement of an object in the absence of any force acting on it.

Note: If the object moves from one place to another place there will be displacement. If there is displacement i.e. if the object moves from one place to another place then it will have velocity but it has to be constant velocity so that there will be no force acting on it.