VITEEE 2017 Paper

The differential equation of the motion is

dv

dt

= 30 - 3v ... (i)
⇒

dv

30−3v

= dt
Integrating we get
-

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

dv

dt

= 0
⇒ 30 - 3v = 0 from (i)
∴ v =

30

3

= 10 cm/s
which is the maximum velocity
However from (ii)

dv

dt

= 3 Ae−3t
Clearly

dv

dt

= 0 if t → ∞