A particle moves according to the equation dvdt = α - β v , where α and β are constants. Find the velocity as a funtion of time. Assume body starts from rest.
Take the relation given for acceleration and integrate with the given limits to obtain the desired function for velocity.
dvdt = α - β v ⇒ v∫1 dvα−βv = t∫0 dt
v = (αβ) (1 - e−βt)