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

Question

If a body starts from rest, the time in which it covers a particular displacement with uniform acceleration is (A) inversely proportional to the square root of the displacement (B) inversely proportional to the displacement (C) directly proportional to the displacement (D) directly proportional to the square root of the displacement

Tardigrade Admin · Accepted Answer

Apply equation of kinematic s = ut +(1/2) at 2 t 2+(2 ut / a )-(2 s / a )=0 t 2+ pt - ks =0 Where, p =(2 u / a ) and k =(2/ a ) t =(- p ± √ p 2+ ks /2) Hence, time is directly proportional to root of displacement.

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

inversely proportional to the square root of the displacement

inversely proportional to the displacement

directly proportional to the displacement

directly proportional to the square root of the displacement

Apply equation of kinematic $s = u t + \frac{1}{2} a t^{2}$
$t^{2} + \frac{2 u t}{a} - \frac{2 s}{a} = 0$
$t^{2} + pt - k s = 0$
Where, $p = \frac{2 u}{a}$ and $k = \frac{2}{a}$
$t = \frac{- p \pm p ^{2} + k s}{2}$
Hence, time is directly proportional to root of displacement.

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

inversely proportional to the square root of the displacement

inversely proportional to the displacement

directly proportional to the displacement

directly proportional to the square root of the displacement

Apply equation of kinematic s=ut+21​at2 t2+a2ut​−a2s​=0 t2+pt−ks=0 Where, p=a2u​ and k=a2​ t=2−p±p2+ks​​ Hence, time is directly proportional to root of displacement.

Apply equation of kinematic $s = u t + \frac{1}{2} a t^{2}$
$t^{2} + \frac{2 u t}{a} - \frac{2 s}{a} = 0$
$t^{2} + pt - k s = 0$
Where, $p = \frac{2 u}{a}$ and $k = \frac{2}{a}$
$t = \frac{- p \pm p ^{2} + k s}{2}$
Hence, time is directly proportional to root of displacement.