Why does kinetic energy increase with the square of velocity?

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I was thinking kinetic energy would behave similarly to momentum. For example a smaller projectile could have much more kinetic energy than a larger one but less momentum. I don’t know that doesnt make much sense to me. If anyone could help me understand it would be much appreciated.

Velocity is increased 3 times by it’s initial velocity, by what factor does its kinetic energy increase?

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If a baseball’s velocity is increased to three times its original velocity, by what factor does its kinetic energy increase?
Thank you, ‘Physics Is Fun,’ that’s what I originally thought.

Why does kinetic energy increase quadratically with velocity?

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I know the mathematical reason why, but suppose I had some sort of car engine that used fuel at a constant rate and applied a constant force to an accelerating mass. As the mass moves faster, it’s kinetic energy increases quadratically, but the fuel is being consumed used at a constant rate, meaning the energy is coming out of the fuel at a steady rate. How does this work? Am I misunderstanding something?

How to know if internal energy increase or decrease? PV Graphs?

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given a pressure volume graph or diagram, is there a way to tell (from one point to the other) of whether or no internal energy is increased is decreased? i know pressure*volume is proportional to Temp

for example if pressure/volume/temp increases or decreases
does the internal energy increase or decrease for each ? is there a way to tell?

Gravitational potential energy increase in a jump?

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The max height a typical person can jump from crouched start is 55 cm. By how much does the gravitational potential energy increase for a 74 kg person in such a jump?

Delta U= ____ J
The second part of the question asks, Where does this energy come from?

Find the velocity of the particle and the total kinetic energy increase in the process?

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An unstable atomic nucleus of mass 16.20 x 10^-27 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.00 x 10^-27 kg, moves along the y axis with a velocity of 6.00 x 10^6 m/s. Another particle, of mass 8.40 x 10^-27 kg, moves along the x axis with a speed of 4.00 x 10^6 m/s. Find the following. Find the velocity of the particle and the total kinetic energy increase in the process.

What is the total energy increase?

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A car with a mass of 1500kg is at rest a t the base of a hill. It accelerates up the incline reaching a speed of 25 m/s at a height of 100m. What is the total increase in mechanical energy (PE + KE) at that point?

Does MetaboLife work for more energy? increase weight loss?

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I feel i am always sleepy, and trying to lose weight and gain more energy, i have started taking these MetaboLife pills that say increased energy..do you think this will work??
I am a student too, do you think they will help keep me alert?

In the particle in a box equation, E = (n^2*h^2)/(8*m*L), why does the energy increase while the mass decrease?

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I understand basically how the equation is derived, I just am wondering if the mass increasing changes a different variable which makes the energy increase, because it seems couterintuitive to me. Thanks for the help.
By einstein’s equation E = mc^2, as the mass of a particle increases its energy should also increase, however in the particle in the box equation the opposite seems to be true, that is why I am confused.

When there is no kinetic energy change, does potential energy increase or decrease?

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When there is no kinetic energy change, does potential energy increase or decrease?

Please help!
uh well we did a lab where the temperature remained constant in water so therefore kinetic energy remained the same

the next questino is asking if the potential energy incrased or decreased witht he kinetic energy staying the same in that situation
thank you!