A particles 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 `(v_(1)+v_(2))//2`. Is this correct ? Substantiate your answer.

Explanation

Consider a particle moving with uniform acceleration a.
At t = 0, the (initial) velocity = `v_(1)`
At t = 0, the (final) velocity = `v_(2)`
time = t
Acceleration, `a=(v_(2)-v_(1))/(t-0)" "[because a=(v_(2)-v_(1))/(t_(2)-t_(1))]`
Displacement `S=v_(1)t+1/2at^(2)" "(because S=ut+1/2at^(2))" "(##VIK_QB_PHY_XI_C03_E05_002_S01.png" width="80%">
`S=v_(1)t+1/2[(v_(2)-v_(1))/t]t^(2)`
`S=t[v_(1)+v_(2)/2-v_(1)/2]=t[(v_(1)+v_(2))/2]S/t=[(v_(1)+v_(2))/2]`
Average velocity = `S/t=(v_(1)+v_(2))/2`
Hence value = `(v_(1)+v_(2))/2`
`therefore` The given statement is true.