Linear Motion:
Consider a particle moving along x axis as shown in Figure, the displacement of this particle can be defined by its x-coordinate measured from fixed refimerence point O.
![1839_img_linear.png](https://www.expertsmind.com/CMSImages/1839_img_linear.png)
When the particle is on the right hand side of O, we can call this displacement positive, and when the particle is on the left hand side of O we can call the displacement negative.
As the particle moves, the displacement varies along time. If the displacement is x at any time t, the motion of the particle can be completely defined by the relation x = f (t), where f (t) stands for a function of time.
The relationship between x and t will based upon how the particle moves along x axis.
If x = x0 + v t
then constant x0 represents an initial displacement at time t = 0, while the constant v represents the rate of increase of displacement. Such motion of a particle is called a uniform rectilinear motion.
Consider a particle at A at time t as shown in Figure. After a small interval of time, Δt, the particle moves further and occupies position B such that
AB = Δ x
Then we may define,
Δ x = Δ t
Average change of displacement, also called as average velocity during time interval Δt.
Δ x/ Δ t as Δ t → 0 is called the instantaneous velocity which can be expressed as dx/ dt
Thus, mathematically the differentiation of x with respect to t gives us the instantaneous velocity.