The acceleration experienced by a moving boat after is engine is cut-off, is given by 𝑎 = −𝑘𝑣3 , where 𝑘 is a constant. If 𝑣0 is the magnitude of velocity at cut-off, then the magnitude of the velocity at time 𝑡 after the cut off is

April 15, 2022

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Physics Problems

Question : The acceleration experienced by a moving boat after is engine is cut-off, is given by 𝑎 = −𝑘𝑣3 , where 𝑘 is a constant. If 𝑣0 is the magnitude of velocity at cut-off, then the magnitude of the velocity at time 𝑡 after the cut off is

(A) $\dfrac{v_{0}}{2ktv_{0}^{2}}$

(B) $\dfrac{v_{0}}{1+2ktv_{0}^{2}}$

(D) $\dfrac{v_{0}}{1+2ktv_{0}^{2}}$

Answer : option (D)

Solution :

The acceleration experienced by a moving boat after is engine is cut-off, is given by 𝑎 = −𝑘𝑣3 , where 𝑘 is a constant. If 𝑣0 is the magnitude of velocity at cut-off, then the magnitude of the velocity at time 𝑡 after the cut off is