Why is kinetic energy equal to half of momentum squared over mass?

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In summary, easy momentum, also known as linear momentum, is the product of an object's mass and its velocity and measures its motion. Kinetic energy is the energy an object possesses due to its motion and is directly proportional to its mass and the square of its velocity. These two quantities are related through the equation <i>p</i> = <i>m</i><i>v</i>, where <i>p</i> is the easy momentum, <i>m</i> is the mass, and <i>v</i> is the velocity. They are important concepts in studying motion in fields such as physics and engineering, and are used to predict object behavior and design efficient machines and structures. Real-world examples include a moving
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tnutty
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I know that :

kinetic energy of something = P^2 / 2m , or momentum squared over 2m


why so?

I see that taking the integral of mv dv = kenitic.

can you prove this to
 
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  • #2
You know p in terms of m and v. You also know E in terms of m and v. This should get you started.
 
  • #3
KE = [tex]\frac{1}{2} mv ^ 2[/tex]

= [tex]\frac{1}{2} pv[/tex]

= [tex]\frac{1}{2} \frac{pmv}{m}[/tex]

= [tex]\frac{1}{2} \frac{p ^ 2}{m}[/tex]
 

What is easy momentum?

Easy momentum, also known as linear momentum, is a physical quantity that measures the motion of an object. It is defined as the product of an object's mass and its velocity.

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is directly proportional to an object's mass and the square of its velocity.

How are easy momentum and kinetic energy related?

Easy momentum and kinetic energy are related through the equation: p = mv, where p is the easy momentum, m is the mass, and v is the velocity. This means that an object with a larger easy momentum also has a greater kinetic energy.

What are some real-world examples of easy momentum and kinetic energy?

An example of easy momentum and kinetic energy can be seen in a moving car. The car's easy momentum is determined by its mass and speed, and its kinetic energy is what allows it to continue moving forward. Another example is a football being kicked, where the player's leg provides the force (easy momentum) and the ball's kinetic energy determines how far it will travel.

How is easy momentum/kinetic energy used in scientific research?

Easy momentum and kinetic energy are important concepts in studying the motion of objects in various fields such as physics, engineering, and biomechanics. They are used to predict the behavior of objects in motion and to design machines and structures that can efficiently utilize these physical quantities.

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