is denoted by t (see Appendix . ). It is the rate of change of position with respect to time, at that instant. We can use Eq.
( .1a) for obtaining the value of velocity at an instant either graphically or numerically . Suppose that we want to obtain graphically the value of velocity at time t = s (point P) for the motion of the car represented in Fig. . calculation.
Let us take ∆ t = s centred at t = s. Then, by the definition of the average velocity, the slope of line P P ( Fig. . ) gives the value of average velocity over the interval s to s.
Fig. . Determining velocity from position-time graph. Velocity at t = s is the slope of the tangent to the graph at that instant .
Now, we decrease the value of ∆ t from s to s. Then line P P becomes Q Q and its slope gives the value of the average velocity over the interval . s to . s.
In the limit ∆ t → , the line P P becomes tangent to the position- time curve at the point P and the velocity at t = s is given by the slope of the tangent at that point. It is difficult to show this process graphically. But if we use numerical method to obtain the value of the velocity, the meaning of the limiting process becomes clear . For the graph shown in Fig.
gives the value of ∆ x / ∆ t calculated for ∆ t equal to . s, . s, . s, .
s and . s centred at t = . s. The second and third columns give the value of t = t and t = and the fourth and the fifth columns give the