Constant rate of acceleration formula

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SUMMARY

The discussion centers on calculating the time and velocity required for a spacecraft to travel 18 million miles (halfway to Mars) while accelerating at a constant rate of 1g (9.8 m/s²). Using the formula for distance, distance = 1/2 * acceleration * time², participants emphasize the need to convert units appropriately before solving for time. Once the time is determined, the final velocity can be calculated using velocity = acceleration * time. This approach provides a clear method for understanding the effects of constant acceleration in space travel.

PREREQUISITES
  • Understanding of basic physics concepts, particularly acceleration and velocity
  • Familiarity with the formula for distance in uniformly accelerated motion
  • Ability to perform unit conversions, especially between miles and meters
  • Basic algebra skills for solving equations
NEXT STEPS
  • Research the implications of constant acceleration in space travel
  • Learn about gravitational effects on spacecraft during long-distance travel
  • Explore advanced kinematic equations for varying acceleration scenarios
  • Investigate real-world applications of artificial gravity in spacecraft design
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in the mathematics of space travel and acceleration effects.

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

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