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

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SUMMARY

The distance formula derived from the acceleration due to gravity is expressed as d = 1/2 gt². This formula originates from the integration of acceleration (a) to obtain velocity (v) and subsequently position (s). The process involves integrating acceleration with respect to time, resulting in the equations v = at + v₀ and s = 0.5at² + v₀t + s₀. Understanding this derivation is essential for both algebra-based and calculus-based physics courses.

PREREQUISITES
  • Understanding of basic calculus, specifically integration
  • Familiarity with kinematic equations in physics
  • Knowledge of the concepts of acceleration and velocity
  • Ability to manipulate algebraic expressions and constants
NEXT STEPS
  • Study the derivation of kinematic equations in physics
  • Learn about the principles of integration in calculus
  • Explore the relationship between acceleration, velocity, and displacement
  • Investigate real-world applications of the distance formula in projectile motion
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Students in physics courses, educators teaching kinematics, and anyone interested in understanding the mathematical foundations of motion under gravity.

Icedfire01
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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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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.]
 
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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