Question

A stone is falling freely and describes a distance $S$ in $t$ seconds given by equation $S=\frac{1}{2}g{t}^2$. The acceleration of the stone is

• A. Uniform
• B. Zero
• C. Non–uniform
• D. Indeterminate

Answer 1

The correct option is A

Uniform

Step 1. Given Data:

Distance covered by stone, $S=\frac{1}{2}g{t}^2$

Time $=t$

Acceleration of the stone $=a$

Step 2. Find the acceleration of the stone:

We have,

$S=\frac{1}{2}g{t}^2$ $\left[\because Given\right]$ …..$\left(i\right)$

Where $S$ is distance, $g$ acceleration due to gravity and $t$ is time.

Now,

Differentiate equation $\left(i\right)$ with respect to the time we get

$\frac{dS}{dt}=\frac{d\left(\frac{1}{2}g{t}^2\right)}{dt}$

Where $\frac{dS}{dt}$ is the velocity of the stone.

$\frac{dS}{dt}=v=gt$ ……..$\left(ii\right)$

Where $v$ is the velocity of the stone.

Again, differentiate equation $\left(ii\right)$ with respect to the time we get.

$\frac{dv}{dt}=\frac{d\left(gt\right)}{dt}$

$\frac{dv}{dt}=a=g$

$a=$constant

Therefore, the acceleration of the stone is uniform.

Hence, option A is correct.