Question

The displacement of a body is given by $s=\frac{1}{2}g{t}^2$, where $g$ is acceleration due to gravity. The velocity of the body at any time $t$ is

• A. $\frac{g{t}^3}{6}$
• B. $\frac{g{t}^2}{6}$
• C. $gt$
• D. $\frac{gt}{2}$

Answer 1

The correct option is C $gt$

Given,

Displacement of body, $s=\frac{1}{2}a{t}^2$

Kinematic equation, $s=ut+\frac{1}{2}a{t}^2$

On comparing, it is clear that acceleration is equal to$a=g$and initial velocity $u=0.$

Apply kinematic equation

$v=u+at$

$v=0+gt$

$v=gt$

Hence, velocity at time $t$ is $gt.$