Constant rate of acceleration formula

[biedul]

This is a question that came up in a conversation with my father who was a fighter pilot in ww2... we got to talking about acceleration as a method of creating artificial gravity during space travel. This is the question: Mars is 36 million miles from Earth at it's closest so if a ship is traveling at a constant rate of 1g, how long would it take to reach the halfway mark (18 million miles) and what would your velocity expressed in MPH would you be traveling? The idea being that the ship would then turn around a decelerate at the same 1g rate. I realize that this is a hypothetical but neither of us have the math skills to solve this fun little question.

 

[Tinyboss]

If you're starting at zero speed and accelerating at a constant rate, then distance = 1/2 * acceleration * time^2. Plug in 36M miles and 9.8m/s^2 (fix the units first!), and solve for time.

 

[CompuChip]

Once you have that, you can find the velocity from
velocity = acceleration * time