# 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

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) $\dfrac{v_{0}}{\sqrt{2v_{0}^{2}kt+1}}$

Solution :

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