Constant rate of acceleration formula

In summary, the question is how long it would take for a ship traveling at a constant rate of 1g to reach the halfway mark of 18 million miles from Earth, and what would be the velocity expressed in MPH. The formula for this would be distance = 1/2 * acceleration * time^2, with the distance being 36 million miles and the acceleration being 9.8m/s^2. Once the time is calculated, the velocity can be found using the formula velocity = acceleration * time.
  • #1
biedul
1
0
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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  • #2
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.
 
  • #3
Once you have that, you can find the velocity from
velocity = acceleration * time
 

1. What is the constant rate of acceleration formula?

The constant rate of acceleration formula is a mathematical equation that is used to calculate the change in velocity of an object over a specific period of time. It is represented as a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval.

2. How is the constant rate of acceleration formula derived?

The constant rate of acceleration formula is derived from the basic definition of acceleration, which is the rate of change of velocity. By rearranging the formula for acceleration (a = (vf - vi) / t), we can solve for any of the three variables: acceleration, final velocity, or time.

3. What are the units of measurement for the constant rate of acceleration formula?

The units of measurement for the constant rate of acceleration formula will depend on the units used for the variables. Generally, acceleration is measured in meters per second squared (m/s^2), velocity is measured in meters per second (m/s), and time is measured in seconds (s).

4. How is the constant rate of acceleration formula used in science?

The constant rate of acceleration formula is used in many areas of science, especially in physics and engineering. It is essential for calculating the motion of objects and predicting their future positions. It is also used to analyze the effects of forces on objects and to design various machines and structures.

5. What are some real-life examples of the constant rate of acceleration formula?

Some real-life examples of the constant rate of acceleration formula include a car accelerating from 0 to 60 mph in a certain amount of time, a ball rolling down an incline, a rocket launching into space, or a person jumping off a diving board. In all of these cases, the object experiences a constant rate of acceleration, and the formula can be used to calculate its velocity at any point in time.

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