Lets say that we have a rocket with an initial mass of 100kg. By expirimentation we find that if we apply thrust for 3 seconds, we consume 1.5kg of fuel and move 3m.
A) What thrust is produced by the rocket?
B.) What is the exit velocity of the gas?
C.) If we wished to accelerate the rocket by 10m/s, how long a burn would we need?
Solution:
a) Let X=the change in position. By using the position equation we know that X is equal to One-half acceleration(a) times time squared. By plugging in numbers, we find that 
or that 
M/sec^2. Since Thrust is mass times acceleration, T=100kg(a) which is equal to 66 2/3 newtons(N)
B.) Since MA=Vg(dm/dt), Vg=ma/(dm/dt). We know from the previous calculation that MA=Thrust=66 2/3N, and by plugging in the appropriate numbers for dm and dt, we find that Vg=70N/.5kg/s=133 1/3m/s
C.) Going back to the original equation, we remember that MA=Thrust=66 2/3N. To solve this problem, we need to break acceleration down into its individual components, dv/dt, which gives us the equation