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Finding Average Velocity

A particle mo...

Question

A particle moves in a straight line with uniform acceleration. Its velocity at time $t = 0$ is $v_{1}$ and at time $t = t$ is $v_{2}$ . The average velocity of the particle in this time interval is ?

\frac{v_{1} + v_{2}}{2 t}

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\frac{v_{1} + v_{2}}{2}

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\frac{v_{1} + v_{2}}{t}

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None of the above

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Solution

The correct option is B $\frac{v_{1} + v_{2}}{2}$
Average velocity = $\frac{T o t a l d i s t a n c e}{T o t a l t i m e}$
Now, total time=t.
Also, $v_{2} = v_{1} + a t$ or $a = \frac{v_{2} - v_{1}}{t}$
Thus, $s = \frac{v^{2} - u^{2}}{2 a} = \frac{{v_{2}}^{2} - {v_{1}}^{2}}{2 (\frac{v_{2} - v_{1}}{t})}$
Thus, $s = \frac{(v_{2} + v_{1}) t}{2}$
Thus, average velocity is $\frac{(v_{2} + v_{1})}{2}$

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