question_answer

The distance traversed by a moving particle at any instant is half of the product of its velocity and the time of traverse. Show that the acceleration of particle is constant.

Answer:

                We know that instantaneous speed, \[{{\text{v}}_{\text{1}}}=\frac{ds}{dt}\]Where \[\frac{ds}{dt}\]= rate of change of distance. The instantaneous velocity,\[{{\vec{v}}_{i}}=\frac{d\vec{s}}{dt}\] = rate of change of displacement. In one dimensional motion having uniform acceleration, the direction of velocity does not change with time, only the magnitude of velocity changes with time. Therefore, \[|d\vec{s}|=\text{ds}\] or\[{{\text{v}}_{\text{i}}}=\frac{ds}{dt}=\frac{|d\vec{s}|}{dt}=|{{\vec{v}}_{i}}|\].