RRB Paramedical Staff Nurse Model Paper 3

Question : 93 of 100

Marks: +1, -0

A particle moves according to the equation dv/dt = α - β v , where α and β are constants. Find the velocity as a function of time. Assume body starts from rest.

$v=(β{/}α)(1-e^{-β t})$
$v=(β{/}α)(e^{-β t})$
$v=(α{/}β)(1-e^{-β t})$
$v=(α{/}β)(e^{-β t})$

Validate

Solution:

Take the relation given for acceleration and integrate with the given limits to obtain the desired function for velocity.

\;{d v}/{d t}=α-β v ⇒ ∫↙{1}↖{v} \;{d v}/{α-β v}=∫↙{0}↖{t} d t

v=(\;{α}/{β})(1-e^{-β t})

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