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  • The decleration experienced by a moving motor boat, after its engine is cut off is given by <img alt="\mathrm{\frac{d v}{d t}=-k v^3}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cm

The decleration experienced by a moving motor boat, after its engine is cut off is given by \mathrm{\frac{d v}{d t}=-k v^3}, where k is constant .\mathrm{V_0} is the magnitude of the velocity at time t after the cut off. Its velocity is -

Option: 1

\mathrm{\quad V_0 C^{-k t}}


Option: 2

\mathrm{\frac{v_0}{\sqrt{2 v_0^2 k t+1}}}


Option: 3

\mathrm{V_0}


Option: 4

\mathrm{\frac{v_0}{2}}


Answers (1)

best_answer

Given,

 \mathrm{\begin{aligned} &\: \: \: \: \: \: \: \frac{d v}{d t}=-k v^3 \\ &\: \: \int \frac{d v}{v^3}=-k \int_0^t d t \\ & {\left[-\frac{1}{2 v^2}\right]_{r_0}^r=-k[t]_0^t} \end{aligned}}

Or,\mathrm{\frac{1}{2}\left[\frac{1}{V_0^2}-\frac{1}{V^2}\right]=-k t}

\mathrm{\frac{1}{v^2}=\frac{v_0^2}{1+2 k t v_0^2} \text { or } \quad v=\frac{v_0}{\sqrt{2 v_0^2 k t+1}}}

 

 

 

 

Posted by

jitender.kumar

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