Answer:
Option C
Explanation:
The differential equation of the motion is
$\frac{dv}{dt} = 30-3v ...(1)$
$\frac{dv}{30-3v} = dt$
Integrating we get
$-\frac{1}{3} \log_{}{}( 30-3v)=t+C$
log(30-3v) = -3(t +c)
30-3v = $e^{-3t-3c}$ = A$e^{-3t}$, A = $e^{-3c}$
3v = 30 - A$e^{-3t}$ ....(2)
For maximum velocity $\frac{dv}{dt} = 0$
30-3v = 0 from (1)
.'. v = 30/3 = 10 cm/s which is the maximum velocity
However from (2) $\frac{dv}{dt} $= 3A$e^{-3t}$
Clearly $\frac{dv}{dt} $ = 0 , if t →∞
The maximum velocity will be achieved after infinite time in other words, the maximum velocity will never be reached.
