Question

$\dag\sf{ \: KINDLY \: SOLVE \: THE \: QUESTION}$​

Answer 1

Answer:

Option d is correct answer

Explanation:

dv/dt=−kv^3

arranging in variable separable form,

dv/v^3=−kdt

integrating on both sides

gives,

∫dv/v^3=−∫kdt

−1/2v^2=−kt+C………….(2), to find the value of integrating constant C

C

, we want to find the velocity at the time t=0

t=0

, that is at initial velocity.

−1/2v°^2=C…………(3). (v°^2= Magnitude of velocity to cut off)

Hence substituting (3) in (2) gives,

−1/2v2=−kt−1/2v°^2

Rearranging and taking common −1 from both sides we will get,

2v^2=1/kt+1/2v°^2

again rearranging we will get as,

2v^2=2v°^2+1+2ktv°^2

canceling common 2

and taking square roots we get the final velocity as,

v=v°/√1+2ktv°^2

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