# Average vs final speed

1. Sep 12, 2004

### Omid

A rocket can accelerate at an increasing rate as its fuel is consumed and it gets lighter and lighter. If the rocket starts from rest, what can be said about the average speed as compared with the final speed ?
Thanks

2. Sep 12, 2004

### Tide

There's no simple relationship between the final speed and the average speed since the mass of the "rocket" is changing (acceleration is NOT a constant!) until its fuel is completely expelled. You need to actually solve the equation of motion for the rocket and you'll basically find something like
$$v = - v_e \ln \frac {M_{final}}{M_{start}}$$
where $v_e$ is the velocity of the exhaust relative to the rocket. (I'm relying on memory here.)

3. Sep 13, 2004

### amwbonfire

I'll assume this is an explanation question, not a calculation, because you haven't supplied any data.

The average speed is constantly changing, (increasing), because the rocket's acceleration is increasing constantly. The final speed will be very high indeed.

So how can you compare them?

a) Will the final velocity be high or low?
b) What will the average speed of the rocket be?

If you think about it, the final velocity has to be larger than the average speed, because the average takes into account every speed that has occured, while the final speed is going to be the highest speed it reaches. So, comparing them, all you can really say is the final speed will be higher than the average speed.

Andy
AMW Bonfire

4. Sep 13, 2004

### Omid

Thank you very much Andy