How is kinetic energy expressed in terms of mass and velocity?

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Kinetic energy is the energy that an object possesses due to its motion, and it is mathematically expressed as ( E_{\text{kinetic}} = \frac{1}{2} mv^2 ). In this formula, ( m ) represents the mass of the object and ( v ) represents its velocity.

The reason this equation includes the factor of ( \frac{1}{2} ) is rooted in the derivation of kinetic energy from the work-energy principle. When work is done on an object to accelerate it from rest to some velocity ( v ), the work done is equal to the force applied times the distance over which that force is applied. The relationship between force, mass, and acceleration (Newton's second law) leads to the realization that the energy associated with the resulting motion scales with the square of the velocity, yielding that factor of ( \frac{1}{2} ).

Understanding that kinetic energy depends on both mass and the square of velocity is crucial. Increasing either the mass or the velocity of an object will increase its kinetic energy, with the effect of velocity being more pronounced due to the squared term in the equation. Thus, this expression accurately captures how kinetic energy is calculated based on these

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