question_answer

The displacement of a body is given to be proportional to the cube of time elapsed. What is the nature of the acceleration of the body?

Answer:

                Given\[s\propto {{t}^{3}}\] or \[s=k{{t}^{3}}\] \[\therefore \]Velocity\[=\frac{ds}{dt}=3k{{t}^{2}}\] Acceleration \[=\frac{d\upsilon }{dt}=6kt\] i.e.,  acceleration\[\propto t\]. Clearly, the acceleration increases uniformly with time.