The distance a spaceship can travel in space depends on various factors, including the propulsion system, available energy, and the specific mission objectives. Currently, our most advanced spacecraft, such as the Voyager 1 and Voyager 2 probes, have traveled over 22 billion kilometers (13.7 billion miles) and are still operational. However, they were launched in 1977 and have had several decades to accumulate that distance.
The speed at which a spaceship can travel in space depends on the propulsion technology being used. The fastest man-made object to date is the Parker Solar Probe, which is expected to reach speeds of up to 430,000 miles per hour (700,000 kilometers per hour) as it approaches the Sun. However, this is a specific mission designed to study the Sun's environment and is not representative of typical interstellar travel.
For interstellar travel, which involves traveling between stars, the distances are vast, and the speeds required are significantly higher than what we currently achieve. To give you an example, the nearest star system to our solar system, Alpha Centauri, is about 4.37 light-years away, which is roughly 25 trillion miles (40 trillion kilometers). At the speeds we currently achieve with our spacecraft, it would take thousands of years to reach even the nearest star system.
There are several theoretical concepts for faster-than-light travel, such as warp drives and wormholes, but they are purely speculative at this point, and the scientific feasibility and practicality of such technologies are yet to be determined.
It's important to note that space exploration is a rapidly advancing field, and future breakthroughs in propulsion technology or the development of new concepts may enable us to travel greater distances at faster speeds. However, our current capabilities are limited to relatively slow speeds and relatively nearby destinations within our own solar system.