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  • Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by <img alt="\mathrm{X_{P}\left ( t \right )=at+\beta t^{2}}" src="https://entr

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by \mathrm{X_{P}\left ( t \right )=at+\beta t^{2}} and \mathrm{X_{Q}\left ( t \right )=ft-r^{2}} . At what time, both the buses have sam velocity?

Option: 1

\mathrm{\frac{\alpha -f}{1+\beta }}


Option: 2

\mathrm{\frac{\alpha +f}{2\left ( \beta -1 \right )}}


Option: 3

\mathrm{\frac{\alpha +f}{2\left ( 1+\beta \right )}}


Option: 4

\mathrm{\frac{f-\alpha }{2\left (1+ \beta \right )}}


Answers (1)

best_answer

\mathrm{x_{p}(t)=\alpha t+\beta t^{2}}\\

\mathrm{x_{Q}(t)=f t-t^{2}}\\

Velocity of bus  \mathrm{P=V_{p}=\alpha+2 \beta t }

Velocity of bus  \mathrm{Q=V_{Q}=f-2 t}

If  \mathrm{V_{p}=V_{Q} }\\

\mathrm{\alpha+2 \beta t=f-2 t}\\

\mathrm{t(2 \beta+2)=f-\alpha}\\

\mathrm{t=\frac{f-\alpha}{2(\beta+1)}}

Hence the correct answer is option 4.

Posted by

manish painkra

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