How Does the Kinetic Energy Formula Work?

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SUMMARY

The kinetic energy formula, represented as W = mV²/2, defines the work done on an object to accelerate it from rest to a velocity V. The formula incorporates mass (m) and the square of velocity (V²), with the factor of 1/2 arising from the integration of the work done over the change in velocity. The derivation begins with the relationship between force, mass, and acceleration, leading to the conclusion that kinetic energy is directly proportional to both mass and the square of velocity.

PREREQUISITES
  • Understanding of basic physics concepts such as force and acceleration
  • Familiarity with calculus, specifically integration
  • Knowledge of the relationship between work and energy
  • Basic understanding of the variables involved in the kinetic energy formula
NEXT STEPS
  • Study the principles of Newton's laws of motion
  • Learn about the concept of work-energy theorem in physics
  • Explore advanced topics in calculus, focusing on integration techniques
  • Investigate real-world applications of kinetic energy in mechanics
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Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of energy and motion.

herchi
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Hi i would like to know step by step... how the kinetic formula works.
why we multiply by 1/2, by mass, and by v2...what this means?
 
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herchi said:
Hi i would like to know step by step... how the kinetic formula works.
why we multiply by 1/2, by mass, and by v2...what this means?

Start with the definition of the change in kinetic energy
dW=Fdx=m(dV/dt)V(dt)=mVdV (1)
Integrating (1) with the initial condition V=0; W=0
W=mV2/2
Are all your questions answered?
 

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