# Rocket Velocity

1. Jul 31, 2010

### Procrastinate

I am attempting to work out the changing velocity of a rocket on Excel. However, I cannot use the simple:

$$\int{a} dt = v$$.

$$at + C = v$$.

If thrust is constant at 20 000 and the rocket is 2000kg with 600kg not made of fuel and 20kg lost every second, then would the equation be:

$$\int{\frac{20000}{1400-20t}} dt = v$$.

This is forgetting about acceleration due to gravity for the moment.

2. Jul 31, 2010

### Filip Larsen

Your integral is not quite right (you should have delta-v on the right side, not v-dot) and your second equation (delta-v = at) is only correct when acceleration is constant.

For a proper way to model this you want to look at the rocket equation which is derived from the principle of conserved total momentum of the rocket and its ejected mass. You probably want to search for a derivation of this equation in your textbooks or on the net, but otherwise feel free to ask more questions.