A small single-stage rocket is launched vertically as shown in the following figure. Once launched, the rocket

Question:

A small single-stage rocket is launched vertically as shown in the following figure. Once launched, the rocket consumes its fuel, and so its total mass m(t) varies with time t > 0. If it is assumed that the positive direction is upward, air resistance is proportional to the instantaneous velocity v of the rocket, and R is the upward thrust or force generated by the propulsion system, then construct a mathematical model for the velocity v(t) of the rocket.

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