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Assuming an object has a total mass of M and gravitational constant on earth = g,...

Assuming an object has a total mass of M and gravitational constant on earth = g, air resistance = Cd, total surface area = A, initial height = H, and this object has a thruster (assuming constant thrust = F_thrust) that ignites at a time T_ignition and stops burning at time T_turnoff (T_turnoff and T_ignition occur at different time during the process), please derive an equation for the velocity of this linear vertical motion as a function of time, V(t).

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