If a particle traverses a curve path other than straight line, its motion is called curvilinear motion.

Consider Fig. 2.1 (a). The position vector of P at time t is ; . The particle P moves to  P’ in time interval M. The position vector of P’ is r’.

Thus, the point P traverses a displacement ∆ in time M. The average velocity is given

by V=  ∆r /∆t In the limit when ∆t à 0, we get instantaneous velocity

The scalar magnitude of ∆r  is

Average speed    = ∆s / ∆t , Instantaneous speed

Consider, the velocity Vat P and V’ at P’. Thus there is change in V in time from t to t + ∆t [Fig. 2.1 (b)]. This change is shown in Fig. 2.1 (c)

Average acceleration

In the limiting case, the instantaneous acceleration is given by

A is tangent to holograph [Fig. 2.1 (d)] of the motion whereas V is tangential to the path .. of the particle. a in general is not tangent to the path of the particle.

(Adding the tips of the velocities, we get a curve called hodograph)

Fig. 2.1(e)