/sci/ - Science & Math

The problem involves a car with variable mass (M - kt) with initial acceleration = a
The question is: what is the velocity at any time t before the tank is empty?
In the solution, it seems they use the initial value of the force, i.e F at time t=0, on the RHS while differentiating the expression on the LHS without plugging in a value for t.
How can they then proceed to rearrange two equations, one having an explicit value for t (F = Ma) and one having no value plugged in?