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Rectilinear Motion

If the path of the motion of a particle is a straight line, it is called ‘Rectilinear motion

Fig. 1.2 shows the movement of a particle r moving along a straight line. O’ is the initial position of Pat t = 0 and S =S0. P is the position at time t and P’ is the position at time t+ ∆t

Displacement in time                         ∆t =∆S

Displacement m unit time =∆S /∆t


∆S /∆t =v av [Average Velocity]. In the limiting case as ∆t à 0, we have

v = Lt .∆S /∆t= dS /dt , where v is called instantaneous velocity.

v = dS/dt =S

v = v o ­at t =0 (i.e., at initial point 0,)


The average acceleration during ∆t is defined as

a av =∆v / ∆t. In  the limiting case


where a is called the instantaneous acceleration of the particle.

a = dv /dt =v


-a is called instantaneous deceleration or retardation

Thus ,              a d2S / dt = S

From (1.1)                               dt = dS /v and from (1.2) we have

dt = dv / a. thus ,dt = dS /v = dv /a

v dv =a dS