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Q.
If a body starts from rest, the time in which it covers a particular displacement with uniform acceleration is
Motion in a Straight Line
Solution:
Apply equation of kinematic $s = ut +\frac{1}{2} at ^{2}$
$t ^{2}+\frac{2 ut }{ a }-\frac{2 s }{ a }=0$
$t ^{2}+ pt - ks =0$
Where, $p =\frac{2 u }{ a }$ and $k =\frac{2}{ a }$
$t =\frac{- p \pm \sqrt{ p ^{2}+ ks }}{2}$
Hence, time is directly proportional to root of displacement.