First slide
Instantaneous velocity
Question

A particle moves with an initial velocity vo and retardation α v,  where v is its velocity at any time t. The velocity of the particle at time t = 1/α will be

Difficult
Solution

We know that, a = (dv / dt).
Given that a=αv
dvdt=αv or dvv=αdt
Integrating within proper limits, we have
V0vdvv=α0tdt
or logevv0v=α[t]0t
logevlogev0=αt
or logeVV0=αt or VV0=eαt
When t=1/α, we get
v=v0eα×(1/α)=v0e1=v0/e

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