How does the speed of the rocket vary with time if fuel is ejecting at a uniform rate?

Question

A rocket, initially at rest in deep space, starts its thrusters, which then burn and eject fuel at a uniform rate to provide constant thrust to the rocket.

How does the speed of the rocket vary with time?

a) The speed remains constant
b) The speed increases at a constant rate
c) The speed increases at a decreasing rate
d) The speed increases at an increasing rate

Answer 1

The answer is d) The speed increases at an increasing rate or the acceleration of the rocket keeps on increasing with time.
This is because of Newton's Third Law of Motion.
(Mass of Rocket)*(Acceleration of Rocket) = (Mass flow rate of the exhaust gases)*(Velocity of the exhaust gases)
Since all the terms in the RHS of the above equation remain constant and the mass of the rocket keeps on falling, to balance out the equation the acceleration of the rocket has to increase.
That is why a rocket starts off moving slowly and goes faster and faster as it climbs into space