Question

A point moves in a straight line under the retardation

Answer 1

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$\mathfrak{The\:Answer\:is}$

This is known as Uniform Retardation.

$\boxed{Hope\:This\:Helps}$

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Answer 2

Answer:

retardation , a = -Kv , here K is a constant.

we know, retardation = - change in velocity/change in time .

\begin{lgathered}\bf{\frac{dv}{dt}=-Kv}\\\\\implies\int\limits^v_u\frac{dv}{v}=-K\int\limits^t_0{dt}\\\\\implies[lnv]^v_u=-Kt\\\\\implies[lnv-lnu]=-Kt\\\\\implies ln\frac{v}{u}=-Kt\\\\v=ue^{-Kt}\end{lgathered}

dt

dv

=−Kv

⟹

u

∫

v

v

dv

=−K

0

∫

t

dt

⟹[lnv]

u

v

=−Kt

⟹[lnv−lnu]=−Kt

⟹ln

u

v

=−Kt

v=ue

−Kt