# Relationship of kinetic energy and velocity

### Kinetic and Potential Energy

The energy transferred is known as kinetic energy, and it depends on the mass and speed achieved. Kinetic energy can be transferred between objects and. In physics, the kinetic energy of an object is the energy that it possesses due to its motion. Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and . where we have assumed the relationship p = m v and the validity of Newton's Second Law. I guess what you are asking is if you plot the graph of the function: [math]E(v) = \ frac{1}{2}mv^{2} \tag{1}[/math] How would it look like. Well, surprise surprise it.

**Let's Talk Physics: Why is kinetic energy proportional to velocity squared?**

For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction.

Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy.

Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat. Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference.

Thus, the kinetic energy of an object is not invariant. Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space.

- The space bicycle paradox
- Kinetic energy
- Kinetic Energy

However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is elliptical or hyperbolicthen throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance.

Without loss or gain, however, the sum of the kinetic and potential energy remains constant. Kinetic energy can be passed from one object to another.

In the game of billiardsthe player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates its speed as the kinetic energy is passed on to it. Collisions in billiards are effectively elastic collisionsin which kinetic energy is preserved.

Hence its speed increase with respect to B is only about 0, of its first speed increase from immobility on the ground. Let's analyze the case of the bicycles. This is all linear, so I forget about vectors. And we simply do a mostly qualitative analysis to understand what happens.

The rest is just applying formulae. I will assume, to abusively simplify things, that the local surface of Earth is an inertial frame for the small duration of the experiement it is an often used approximation. So we take the local ground as inertial frame for a first analysis. Now bicycle A accelerate again, with the same amount of energy. But if we do the same analysis with respect to buddy bicycle B, things are different.

## What is kinetic energy?

Where is the energy gone? Well, from B's point of view, he is not actually moving: When A was coasting along, he was also motionless with respect to B, until he accelerated again. When, A accelerated, he applied a pushing force on the ground to go forward, which was balanced by a friction reaction force from the ground. It is the reaction force that does the work accelerating A over a distance.

In the Earth frame. Earth is not moving so that no force attached to Earth does any work.

But in buddy B frame, the Earth is actually moving backward. The friction force of A acceleration increases the momentum of A, and this increase has to be stolen somewhere total momentum does not change.

So it has to come from Earth, i. The missing part of the energy has been used to accelerate the Earth motion with respect to B. High speed is easy in space is it?

### Kinetic energy - Wikipedia

Taking the same problem to space, as much as make sense you will see whymay clarify some issues. But it is really quite different. The only way to accelerate is to exchange momentum with another mass. Other than direct use of the natural force fields such as gravitythe usual way to do that is by exhausting a reaction mass at speed from a rocket engine.

You throw the mass one way, and you are pushed the other way with the inverse momentum variation.

Since you carry the mass, the trick is often to increase the exhausted momentum by using high speed with small massesso that you do not end up massless too quickly unless you are a top model. You may have a screen dial telling you how much energy you spent.

But that is of limited use because it will not tell you what you spent it on, as you are accelerating both your craft and the exhausted reaction mass.

The repartition of energy is controled by momentum preservation so that we have in the initial inertial frame as is well known: We can now address the first question: The answer is almost yes in classical mechanicsprovided all other things on board are kept equal. What is true is that the craft will always gain the same amount of velocity with respect to its previous inertial frame, provided it spends its energy in the same way.

The sharing ratio remains open with the data provided here, and so does the velocity increase.