Question

3. A particle moving in a straight line starts
with a velocity u. Its retardation at any
instant is proportional to the displacement,
then its displacement before coming to rest
is (retardation at unit displacement is u)​

Answer 1

Answer:

s = ± $V/\sqrt{u}$

Explanation:

Given: a ∝ s

a = μs

dv/dt = μs

Multiplying and dividing by ds

dv/dt * ds/ds = μs

dv/ds * ds/dt = μs

dv/ds * V = μs

Vdv = μs*ds

Integerating on both sides, we get

$\frac{V^2}{2} = \frac{s^2}{2}$ *μ

From here, s =± $V/\sqrt{u}$