Question

a particle moves rectilinearly with uniform acceleration. Its velocity at time t=0 is v1 and at t=t is v2 then average velocity of the particle in this time interval is v avg = v1 +v2/2 , is this true? ​prove it....

Answer 1

$\sf Average\: velocity = \dfrac{Now,\:total\:distance}{Total\:time}$

$\sf Total\:time = t$

$\sf Also,\:v_2 = v_1 + at\:or\:a =\dfrac{v_2-v_1}{t}$

$\sf Thus,\:s = \dfrac{v^2-u^2}{2a} = \dfrac{ {v_2}^{2} - {v_1}^{2} }{ 2(\dfrac{v_2 - v_1}{t})}$

$\sf Thus,\:s = \dfrac {(v_2 + v_1)t}{2}$

$\sf Thus,\: average\:velocity\:is \dfrac {(v_2 + v_1)}{2}$

$\sf Hence,\:Proved$