question_answer

                                    Two straight lines drawn on the same displacement - time graph make angles\[30{}^\circ \] and \[\text{6}0{}^\circ \] with time-axis respectively  Fig. 2(a).25. Which Une represents greater velocity? What is the ratio of two velocities?

Answer:

                                  Since the slope of the displacement - time graph of uniform  motion in one dimension represents the  velocity of the object, hence the line showing greater slope in graph corresponds to greater velocity of the object. Therefore, the line making angle 60° with time axis represents greater velocity:              Ratio of two velocities;                                 \[\frac{{{\upsilon }_{A}}}{{{\upsilon }_{B}}}=\frac{\tan {{30}^{o}}}{\tan {{60}^{o}}}=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}\]