For a body moving with uniform acceleration $a$ , initial and final velocities in a time interval $t$ are $u$ and $v$ respectively. Then, its average velocity in the time interval $t$ is :

(v + \frac{a t}{2})

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(v - \frac{a t}{2})

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(v - a t)

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(u + \frac{a t}{2})

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Solution

The correct options are
B $(v - \frac{a t}{2})$
D $(u + \frac{a t}{2})$
$S = u t + \frac{1}{2} a t^{2}$
$v = u + a t$
Average velocity $= \frac{T o t a l d i s p l a c e m e n t (s)}{T o t a l t i m e (t)}$ $= \frac{u t + \frac{1}{2} a t^{2}}{t} = u + \frac{1}{2} a t$
Substitute, $u = v - a t$ in the above expression:
We get average velocity $= v - a t + \frac{1}{2} a t = v - \frac{1}{2} a t$
Thus, two options are correct.

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For a body moving with uniform acceleration a, initial and final velocities in a time interval t are u and v respectively. Then, its average velocity in the time interval t is :

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For a body moving with uniform acceleration $a$ , initial and final velocities in a time interval $t$ are $u$ and $v$ respectively. Then, its average velocity in the time interval $t$ is :