Question

A body starts from rest and move with uniform acceleration a for tine t. the average velocity over time t is

Answer 1

since acceleration =velocity/time
hence velocity = acceleration *time
i. e. v=a*t

Answer 2

The answer to the question is $\ \frac{at}{2}$  

CALCULATION:

As per the question, the body starts from rest.

Hence, initial velocity of the body u = 0.

The acceleration of the body is given as a .

The time taken by the body is given as t.

Let the distance covered by the body in time t is S.

From equation of kinematics, we know that-

                                $S=\ ut\ +\ \frac{1}{2}at^2$

                               ⇒ $S=\ 0\times t+\frac{1}{2}at^2$

                                ⇒$S=\ \frac{1}{2}at^2$

The average velocity of a body is defined as the ratio of total distance travelled to total time taken.

Mathematically  $V_{avg}=\ \frac{total\ dfistance}{total\ time}$

                                 $=\ \frac{S}{t}$

                                 $=\ \frac{\frac{1}{2}at^2} {t}$

                                 $=\ \frac{at}{2}$                 [ans]