$A$ body is moving along a straight line with initial velocity $v_0$. Its acceleration $a$ is constant. After $t$ seconds,its velocity becomes $v$. The average velocity of the body over the given time interval is

• A
  $\bar{v}=\frac{v^2-v_0^2}{a t}$
• B
  $\bar{v}=\frac{v^2+v_0^2}{2 a t}$
• C
  $\bar{v}=\frac{v^2+v_0^2}{a t}$
• D
  $\bar{v}=\frac{v^2-v_0^2}{2 a t}$