The speed required for a spacecraft to escape the gravitational pull of the Sun and leave the solar system entirely depends on several factors, including the trajectory, the starting point, and the desired destination. The most common measure used to determine this speed is the escape velocity.
The escape velocity is the minimum speed required for an object to overcome the gravitational pull of a celestial body and escape its influence entirely. For a spacecraft leaving the solar system from Earth's vicinity, the escape velocity from the Sun is approximately 42.1 kilometers per second (km/s) or 93,955 miles per hour (mph).
However, it's important to note that achieving escape velocity alone is not sufficient for interstellar travel. The spacecraft would also require a trajectory and propulsion system capable of achieving the desired speed and direction to reach its intended destination outside the solar system.
In practice, spacecraft leaving the solar system, such as NASA's Voyager 1 and Voyager 2, have utilized gravity assists from planetary flybys to gain additional speed and alter their trajectories. These missions have achieved velocities of around 17-20 km/s (38,000-45,000 mph) relative to the Sun with the help of these gravity assists.
To summarize, the specific speed required for a spacecraft to escape the solar system depends on various factors, but as a general guideline, it would need to attain a velocity of at least 42.1 km/s (93,955 mph) relative to the Sun to overcome its gravitational pull.