question_answer

Two straight lines drawn on the same displacement-time graph make angles \[\mathbf{30}{}^\circ \]and \[\mathbf{60}{}^\circ \] with time-axis respectively, as shown in Fig. Which line represents greater velocity? What is the ratio of the two velocities?                                 

Answer:

                Slope of displacement-time graph \[=\]Velocity of the object As slope of line \[OB\text{ }>\]slope of line \[\text{OA}\] \[\therefore \]The line making angle of \[\text{6}0{}^\circ \] with time-axis represents greater velocity. Ratio of the two velocities \[=\frac{{{\upsilon }_{A}}}{{{\upsilon }_{B}}}=\frac{\tan {{30}^{\circ }}}{\tan {{60}^{\circ }}}\] \[=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}=\mathbf{1:3}\mathbf{.}\]