$2.-$ Rockets accelerate due to the exhaust thrust generated by burning a mass m of fuel $($see the Figure$).$ In take$-$off, thrust acts against gravity in order to reach the velocity for the rocket to escape from Earth. If the thrust force is proportional to the rate of fuel mass loss, write down an equation for the rocket motion at take$-$off. Explain.

Figure $1$: Rocket take$-$off