Question

If a body starts from rest,the time in which it covers a particular displacement with uniform acceleration

• A. inversely proportional to the square root of the displacement
• B. inversely proportional to the displacement
• C. diretily proportional to the displacement
• D. directly proportional to the square root of the displacement

Answer 1

The correct option is D directly proportional to the square root of the displacement

Apply equation of kinematic

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

$t^2+\frac{2ut}{a}-\frac{2s}{a}=0$

$t^2+pt-ks=0$

Where, $p=\frac{2u}{a}andk=\frac{2}{a}$

$t=\frac{-p\pm \sqrt{p^2+ks}}{2}$

Hence, time is directly proportional to root of displacement.