A Speck Of Dust!

this is a variable mass system. so apart from change in velocity, change in mass also contributes to the net force. here, i use newton's second law of motion and little bit of differential calculus

---

Moderator's edits :

If rate of mass accumulation is $A$ ,

$m(t) = At$ where $m(t)$ is instanteous mass of the Gpeck(?),

$F_\text{ent} = \dfrac{d\vec p}{dt} , \vec p = \text{ momentum } = m \vec v$

$F_\text{ent} = \dfrac{d m\vec v}{dt} = m \dfrac {dv}{dt } + v \dfrac {dm}{dt}$

$mg = m \dfrac{dv}{ft} + v \dfrac{dm}{dt}$

$Atg = At \dfrac{dv}{dt} + vA \Rightarrow gt = \dfrac{ t \; dv + v \; dt}{dt} = \dfrac{d tv}{dt}$

$gt \; dt = dv \; t \Rightarrow \int tg \, dt = \int dv \, t$

$\dfrac{gt^2}2 = vt \Rightarrow v = \dfrac{gt}2$

$a = \dfrac{dv}{dt} = \dfrac g2 = 5 \text { ms}^{-2}$ .