There is no limit on speed of a rocket, imposed by physics
(other then speed of light, of course).
Practical limits are given first
by amount of fuel and then
by method of propulsion.
Here is an overview from NASA:
Rocket technology is fundamentally limited by its need for propellant.
The farther, faster, or more payload carried, the more propellant that
is required. This limit cannot be overcome with engineering
refinements. This limitation is based on the underlying physical
principles of all rocket propulsion - the very physics of its
Note, this "physical principles" refer to amount of fuel.
The Relativistic Rocket is possible:
main question still is:
How much fuel is needed?
The secondary questions is: method of propulsion:
EP is faster then CP
The ejection of gases from this reaction provides thrust to the
rocket. The energy provided in chemical propulsion is limited because
it takes a relatively large mass of fuel to achieve the needed levels.
That limits the exhaust velocity. In the space shuttle, for example,
the natural limit imposed by CP is less than three miles a second or
about 10,000 miles per hour."
"In one form of electric propulsion, electro thermal, we use an arc
that has about the energy density of a lightning bolt in heat. So the
speed limit jumps to about 45,000 miles per hour." Ion propulsion
introduces even more energy and can go to 100,000 mph now, with faster
speeds on the horizon.
The short answer: a rocket's speed is limited by the fuel it can carry.
The long answer: read hear:
The final proof (in case of argument) that there is no such limit
(even if slow method, such as CP, is used) comes from physics:
Conservation of momentum:
If you expel a mas m at speed v from moving body (a rocket),
then momentum of that body (rocket) MUST increase by m*v .
No matter how small that v was, it is a positive increase of velocity.
If v is small, then we are wasting resources.
If speed of rocket is [very] high (relativistic) ,
then adding of momentum and relation of momentums and velocity
has to use relativistic formula.
Contribution is still positive. That's all.