Need to derive the distance formula from the acceleration due to gravity

In summary, the distance formula from the acceleration due to gravity is a mathematical equation that calculates the distance an object has fallen due to the acceleration of gravity. It is derived from the equation d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is the time. The acceleration due to gravity is typically measured using an accelerometer or can be calculated using the equation g = F/m. This formula can be used to calculate the distance of an object on other planets, but will need to be adjusted for the different value of g. Air resistance can affect the formula by decreasing the acceleration due to gravity and requiring the formula to include the force of air resistance. Real-life
  • #1
Icedfire01
4
0
Pretty much like the title says. I'm having a hard time finding where the formula: d=1/2gt^2 comes from. Any help would be greatly appreciated.
 
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  • #2
What facts or definitions do you have to start with? (Are you taking an algebra-based or calculus-based course?)
[By the way, post your question in only one thread.]
 
  • #3
Start with acceleration, "a." You know that the second derivative of "a" is "s'', where "s" is the position. Integrate twice and adjust for the constants.

∫a dt = at+v0 = v

∫v dt = .5at2+v0t+s0 = s
 
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1. What is the distance formula from the acceleration due to gravity and how is it derived?

The distance formula from the acceleration due to gravity is a mathematical equation that calculates the distance an object has fallen due to the acceleration of gravity. It is derived from the equation d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is the time.

2. How is the acceleration due to gravity measured?

The acceleration due to gravity is typically measured using a device called an accelerometer. This device measures the acceleration of an object due to the force of gravity. It can also be calculated using the equation g = F/m, where g is the acceleration due to gravity, F is the force of gravity, and m is the mass of the object.

3. Can the distance formula from the acceleration due to gravity be used to calculate the distance of an object on other planets?

Yes, the distance formula from the acceleration due to gravity can be used to calculate the distance of an object on other planets. However, the value of g will be different on different planets, so the formula will need to be adjusted accordingly.

4. How does air resistance affect the distance formula from the acceleration due to gravity?

Air resistance can affect the distance formula from the acceleration due to gravity by slowing down the object's descent and reducing the acceleration due to gravity. In this case, the distance formula would need to be modified to include the force of air resistance in the equation.

5. What are some real-life applications of the distance formula from the acceleration due to gravity?

The distance formula from the acceleration due to gravity has many real-life applications, such as calculating the distance a skydiver falls before deploying their parachute, predicting the trajectory of a projectile, and determining the height of a building using a falling object. It is also used in the field of physics to study the effects of gravity on objects.

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