Classical Mechanics - basics are fun

The flatcar has an initial mass $M$ and an initial unspecified speed to the right. I assume that to be zero. Mass is added to the flatcar at a rate $n$ . Therefore, the mass of the car at any instant is:

$m = M + nt$

Applying Newton's second law to the flatcar as follows. Net force is equal to the rate of change of linear momentum.

$\frac{d}{dt}\left(mv\right) = F$ $\frac{d}{dt}\left((M+nt)v\right) = F$

$\implies d \ \left((M+nt)v\right) = F \ dt$ $\implies \int_{0}^{(M+nt)v} d \ \left((M+nt)v\right) = \int_{0}^{t}F \ dt$

Solving and rearranging:

$v = \frac{Ft}{M+nt}= \frac{F}{Mt^{-1} + n}$ $a = 1 \ ; \ b = -1 \ ; \ c = 1$

using principle of impulse and momentum, the impulse imparted by the force equals the momentum of the combined mass,

F t = (M + n t) v

this will give an answer of 3. easy