question_answer

The deceleration experienced by a moving motorboat after its engine is cut off, is given by \[\frac{\text{dv}}{\text{dt}}\text{ = -K}{{\text{V}}^{3}}\]  where K is constant. If \[{{V}_{0}}\] is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time t after the cut-off is

A) \[\frac{{{V}_{0}}}{\sqrt{\left( 2V_{0}^{2}Kt+1 \right)}}\]

B) \[{{V}_{0}}{{e}^{-Kt}}\]

C) \[{{V}_{0}}/2\] 

D) \[{{V}_{0}}\]