I have encountered the following difficulty while solving problems in the variable mass dynamics. One of them said that we have a buggy with sand, of mass $m_0$ initially, with a rate of mass loss $\mu$. The buggy is pulled with a constant force $\vec{F}$.
Of course we may say that: $$\frac{dm}{dt} = -\mu$$
My approach was to apply Newton's law like this: $$\frac{d\vec{p}}{dt}=\vec{F} \to (m_0 -\mu t) \frac{d\vec{v}}{dt} - \mu \vec{v} = \vec{F}$$
However, the solution of the problem said that we may write Newton's Law like this: $$m\vec{a} = \vec{F} \to (m_0 - \mu t) \frac{d\vec{v}}{dt} =\vec{F}$$
Which of them is the correct and why?
