If you were to travel at a constant acceleration of 1g (which is equivalent to the acceleration due to gravity on Earth's surface) for a period of 75 years, the distance you would cover in space-time can be calculated using the equations of motion from special relativity.
Assuming you are starting from rest and neglecting relativistic effects due to high speeds, the distance covered can be approximated using the equation:
d = (1/2) * a * t^2
where: d is the distance covered, a is the constant acceleration (1g ≈ 9.8 m/s^2), and t is the time of acceleration (75 years = 75 * 365.25 * 24 * 60 * 60 seconds).
Plugging in the values, we have:
d = (1/2) * 9.8 m/s^2 * (75 * 365.25 * 24 * 60 * 60 s)^2
Evaluating this equation gives you the approximate distance covered. However, it's important to note that this calculation assumes a constant acceleration, which is not physically feasible for a human spacecraft over such a long duration. Additionally, relativistic effects would become significant at high speeds, requiring more sophisticated calculations. Nonetheless, as a rough estimate, this calculation can provide an order of magnitude for the distance traveled.