Question

A body starting from rest moves with uniform acceleration. The distance covered by the body in time $t$ is proportional to

• A. $\sqrt{t}$
• B. $t^{\frac{3}{2}}$
• C. $t^{\frac{2}{3}}$
• D. $t^2$

Answer 1

The correct option is D

$t^2$

Step 1. Given data:

The initial velocity of body, $u=0m/s$ [As body starts from rest]

Uniform acceleration, $a$ in $m/s^2$

Time $t$

Step 2. Formula used:

Third equation of motion for uniform acceleration, $S=ut+\frac{1}{2}a{t}^2$

Step 3. Calculate the distance covered in time t

Substituting the values in the above equation, $S=0\times t+\frac{1}{2}a{t}^2$

$S=\frac{1}{2}a{t}^2$

$\Rightarrow S\propto$ $t^2$

Therefore, the distance covered is directly proportional to the square of the time.

Hence, the Option $\left(D\right)$ is correct.