What does the slope of 'position - time' graph represent? Which physical quantity is obtained from it?

Explanation

(i) Graphically the slope of the position - time graph will give the velocity of the particle.
(ii) At the same time, if velocity - time graph is given, the distance and displacement are determined, by calculating the area under the curve.
Velocity is given by `(dx)/(dt)=v`.
(iii) Therefore, `dx=vdt`
By integrating both sides, `int_(x_(1))^(x_(2))dx=int_(x_(1))^(x_(2))vdt`
Integration is equivalent to area under the given curve.
(iv) So the term `int_(t_(1))^(t_(2))vdt` represents the area under the curve v as a function of time.
(v) Since the left and hand side of the integration represents the displacement travelled by the particle from time `t_(1)` to `t_(2)` the area under the velocity time graph will given the displacement of the particle.


(vi) If the area is negative, it means that displacement is negative, so the particle has travelled in the negative direction.