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  • An automobile of mass accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :Option: 1 <img alt="\left(\

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :
Option: 1 \left(\frac{9 P}{8 m}\right)^{\frac{1}{2}} t^{\frac{3}{2}}
Option: 2 \left(\frac{8 \mathrm{P}}{9 \mathrm{~m}}\right)^{\frac{1}{2}} \mathrm{t}^{\frac{2}{3}}
Option: 3 \left(\frac{9 \mathrm{~m}}{8 \mathrm{P}}\right)^{\frac{1}{2}} \mathrm{t}^{\frac{3}{2}}
Option: 4 \left(\frac{8 P}{9 m}\right)^{\frac{1}{2}} t^{\frac{3}{2}}

Answers (1)

best_answer

u=0

power =p= constant

P=\left(m \frac{d v}{d t}\right) v

p d t=m v d v

\begin{gathered} \int_{0}^{p d t} v d v=\frac{p}{m} \int_{0}^{t} d t \\ \end{gathered}

\begin{gathered} \left [ \frac{v^{2}}{2} \right ] =\frac{p}{m}t \end{gathered}

\begin{aligned} &v=\left(\frac{2 p}{m}\right)^{1 / 2} t^{1 / 2} \\ &\frac{d s}{d t}=\left(\frac{2 p}{m}\right)^{1 / 2} t^{1 / 2} \\ &d s=\left(\frac{2 p}{m}\right)^{1 / 2} t^{1 / 2} d t \\ &s=\left(\frac{2 p}{m}\right)^{1 / 2} \frac{t^{3 / 2}}{3 / 2} \\ \end{aligned}

\begin{aligned} &\Rightarrow s=\left(\frac{8 p}{g m}\right)^{1 / 2} t^{3 / 2} \end{aligned}

 

Posted by

vishal kumar

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