A particle is moving with speed \upsilon =b\sqrt{x} along the positive x-axis. Calculate the speed of the particle at timet=\tau(assume that the particle is at the origin at t=0).

 

  • Option 1)

    \frac{b^{2}\tau}{4}

     

     

     

  • Option 2)

    \frac{b^{2}\tau}{2}

  • Option 3)

    b^{2}\tau

  • Option 4)

    \frac{b^{2}\tau}{\sqrt{2}}

Answers (1)

V=b\sqrt{x}

\frac{dx}{dt}=b\sqrt{x}

\int _{o}^{x}\frac{dx}{\sqrt{x}}=b\int ^{t}_{o}dt

2\sqrt{x}=bt

x=\frac{b^{2}t^{2}}{4}\cdots (a)

\frac{dx}{dt}=\frac{b^2t}{2}\cdots (b)

V=\frac{b^{2}\tau}{2}


Option 1)

\frac{b^{2}\tau}{4}

 

 

 

Option 2)

\frac{b^{2}\tau}{2}

Option 3)

b^{2}\tau

Option 4)

\frac{b^{2}\tau}{\sqrt{2}}

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