VITEEE 2017 Paper

The differential equation of the motion is $\frac{dv}{dt}$ = 30 - 3v ... (i) ⇒ $\frac{dv}{30-3v}$ = dt Integrating we get - $\frac{1}{3}$ log (30 - 3v) = t + C ⇒ log (30 - 3v) = -3(t + c) ⇒ 30 - 3v = $e^{-3t-3c}$ = $Ae^{-3t}$ , A = $e^{-3c}$ ⇒ 3v = 30 - $Ae^{-t}$ ... (ii) For maximum velocity $\frac{dv}{dt}$ = 0 ⇒ 30 - 3v = 0 from (i) ∴ v = $\frac{30}{3}$ = 10 cm/s which is the maximum velocity However from (ii) $\frac{dv}{dt}$ = 3 $Ae^{-3t}$ Clearly $\frac{dv}{dt}$ = 0 if t → ∞