Question : The retardation experienced by a moving motor boat, after its engine is cut off, is given by 𝑑𝑢 𝑑𝑡 = −𝑘𝑣 3 , where 𝑘 is a constant. If 𝑣0 is the magnitude of the velocity at cut-off, the magnitude of the velocity at time 𝑡 after the cut-off is
(A) v_{0}
(B) \dfrac{v_{0}}{2}
(C) v_{0}e^{-kt}
(D) \dfrac{v_{0}}{\sqrt{2v_{0}^{2}kt+1}}
Answer : option (D)
Solution :
