Question

Average velocity of a particle moving in a straight line, with constant acceleration $a$ and initial velocity $u$ in first $t$ seconds is:

• A. $u$
• B. $u+at$
• C. $u+\frac{at}{2}$
• D. $\frac{u+at}{2}$

Answer 1

The correct option is C

$u+\frac{at}{2}$

Given, initial velocity is $u$, acceleration is $a$ and total time taken is $t$.
Let $s$ be the displacement of the particle.
From second equation of motion,
$s=ut+\frac{1}{2}a{t}^2$.
$AverageVelocity=\frac{Totaldisplacement}{Totaltime}$

$\therefore$ $Averagevelocity=\frac{ut+\frac{{at}^2}{2}}{t}$
$=u+\frac{at}{2}$