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the retardation experienced by a moving motor boat after its,engine is cutoff at the instant t is given by a= -kV 4 , where k is a contant. if v o is the magnitude of velocity at the cutoff, find the magnitude of velocity at time t after the cutoff.

the retardation experienced by a moving motor boat after its,engine is cutoff at the instant t is given by a= -kV4 , where k is a contant. if vo is the magnitude of velocity at the cutoff, find the magnitude of velocity at time t after the cutoff.

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

Since we know that the acceleration of the body is the rate of change of its velocity, we have

a=\dfrac{dv}{dt}=-kv^4
\implies \int_v_0^v\dfrac{dv}{v^4}=-k\int_0^t dt
\implies \dfrac{1}{-3}(\dfrac{1}{v^3}-\dfrac{1}{v_0^3})=-kt
\implies \dfrac{1}{v^3}-\dfrac{1}{v_0^3}=3kt \implies \dfrac{1}{v^3}=\dfrac{1}{v_0^3}+3kt

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