How Do You Derive Formulas from the Work-Kinetic Energy Theorem?

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SUMMARY

The discussion focuses on deriving formulas from the Work-Kinetic Energy Theorem, specifically the relationships between force, distance, mass, and velocity. The established equations include: Force (F = (1/2)mv²/d), Distance (d = (1/2)mv²/F), Mass (m = 2Fd/v²), Velocity squared (v² = 2Fd/m), and Velocity (v = √(2Fd/m)). All derived formulas are confirmed to be correct, providing a comprehensive understanding of the theorem's applications in physics.

PREREQUISITES
  • Understanding of the Work-Kinetic Energy Theorem
  • Familiarity with basic physics equations
  • Knowledge of algebraic manipulation
  • Concept of force, mass, and acceleration
NEXT STEPS
  • Study the implications of the Work-Energy Principle in different physical scenarios
  • Explore advanced applications of kinetic energy in real-world problems
  • Learn about potential energy and its relationship with kinetic energy
  • Investigate the conservation of energy in closed systems
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Students studying physics, educators teaching mechanics, and anyone interested in understanding the principles of energy and motion.

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Homework Statement


We have Work=Kinetic Energy which is :
##A=E_k=Fd=\frac{1}{2}mv^2##
Find formulas of :
Force, distance, mass, velocity squared and velocity

Homework Equations


##A=E_k=Fd=\frac{1}{2}mv^2##

The Attempt at a Solution


##F=\frac{\frac{1}{2}mv^2}{d}##

##d=\frac{\frac{1}{2}mv^2}{F}##

##m=\frac{2Fd}{v^2}##

##v^2=\frac{2Fd}{m}##

##v=\sqrt{\frac{2Fd}{m}}##

Are all the formulas right found? Thanks ;)
 
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