Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Physics Does constant velocity mean no acceleration? Ben Davis March 16, Does constant velocity mean no acceleration? Is there work with constant velocity? What is the difference between constant acceleration and constant velocity?
What are the three types of velocity? What are the 2 types of velocity? Acceleration is the rate of change of velocity with time. Like velocity, this is a vector quantity that has a direction as well as a magnitude.
An increase in velocity is commonly called acceleration while a decrease in velocity is sometimes termed deceleration. Technically, since velocity includes a direction as well as a speed, a change in direction at a constant speed is still considered acceleration. Acceleration can be defined simply as:. Alternatively, you can find it by taking the second derivative of the expression for position with respect to time.
If you have a constant velocity, this means you have zero acceleration. You can imagine this as driving down a straight road but keeping your speedometer on the same value. A constant acceleration is quite different. The acceleration due to gravity on the Earth has the constant value 9. The velocity starts low, but increases by 9. However, acceleration is the key characteristic here, not velocity. That is a description of an emergent property , in the same way that pressure and temperature of the gas laws are not really properties of single particles but emerge from the interaction of all the particles.
As far as spacetime is concerned, acceleration and gravity are similar things. A charged particle that is accelerating is basically experiencing a force.
Em waves are nothing but the transmission of a disturbance in the electromagnetic field of the charge. If you consider velocity and acceleration from a purely kinematical point of view, there is no fundamental difference between them.
One is the first time derivative of the location, the other the second. Two accelerating objects comoving with each other will be at rest relatively to each other as much as two objects with the same constant velocity. Classically, EM radiation is purely an observer dependent effect, consisting of those components of the EM field related to the acceleration relative to the observer.
The particle itself assuming it is a point particle can not possibly 'know' whether it is accelerating or not. To be perfectly honest - physics does not know the answer to your question. It seems mysterious to me, too, that the particle would have information on how fast it moved in the past.
There is no strict logical inconsistency, so maybe we just have to satisfy ourselves with "that is what we have observed".
But maybe there is an underlying mechanism we have not yet understood. This reminds me a lot of a problem that bothered Newton about his theory of gravity - how does the planet orbiting a star "know" about the star's gravity, and especially changes in that gravity as the star's location shifts? This was later better understood in light of general relativity, and there were of course more underlying mechanisms to be understood.
I think different subfields of physics will give you different ways of thinking about what parts of the system "know" what. Different formalisms might give different answers as to where this information is stored in the particles?
From the perspective of statistical mechanics, each particle carries "knows" 6 pieces of information: the three components of its position and the three components of its velocity. Equivalently, you can say the three components of its position and the three components of momentum.
For these six pieces of information, there is a kind of memory. So you need no memory for the acceleration. If you code a molecular dynamics simulation maybe simulation of ions in a plasma?
Equivalently, you can have an array of the 3D positions at the current time and another array of the 3D positions at the previous time. You need to keep these arrays from one time step to the next, while the forces and accelerations do not need to be kept.
You then calculate the change in velocity for this particle from the gradient of the potential energy for this particle's positions the force. The potential energy is calculated as a function of all particle positions. This gets more complicated if you include relativistic effects and radiation, because then you need to include the state of the fields or the state of the system at previous times retarded time.
The Feynman-Heaviside formula does seem to need to know about the position, velocity, and acceleration at the retarded time. From a quantum perspective the information about the current speed of a particle is encoded in the wavefunction. See for example the following wave packet of a one dimensional particle. The blue line shows the wavefunction; the distance to the black line shows the amplitude and the angle shows the phase.
The number of turns it makes is proportional to the momentum: when the blue line is rotated more times around the black line the particle moves more quickly. To answer your question, if the universe wants to know the speed of a particle it can just look at the wave function. If this speed is increasing the particle is accelerating. This is a tricky concept. We learn so many times that objects have no objective sense of their own velocity that it starts to feel weird that objects do appear to have an objective measurable notion of their own acceleration.
Your EM radiation from an accelerating particle is one example, radio emission from rotating magnetic stars is another. I think that the cleanest answer is this. From Newton's second law we know that an acceleration is related to an external force.
So the particle "knows it is accelerating" because it is subject to this external force from some other particle s. This is not entirely satisfying when rotating bodies are involved. Two cannon-balls that are roped together in an otherwise empty universe could be spinning around their centre, with a related tension in the rope, or they could be sill with no tension.
These two situations are in our best theories physically distinct, but it is a bit of a puzzle exactly what the rotation is to be defined with respect to given that the example supposes their is nothing else to compare to. See Tim Maudlin's book "Space and Time" for a very interesting account of the cannonballs. I think your question goes to the heart of what we classify as epistemological or ontological, and likely a very beautiful mystery of the universe.
I'd say the answer to your question boils down to information vs dynamic. Informally, take information as one value in multi-dimensional phase space whereas dynamic would correspond to how these values change with time. Velocity and position are information, whereas acceleration is dynamic. That is so most of the time in physics even though they are naturally related by time derivatives velocity is how position varies in time and acceleration is how velocity varies in time.
For some reason, nature has chosen second-order time-derivatives to describe dynamic of systems most of the time. Maybe because with this, any given acceleration as a function of time will always yield a smooth trajectory. So the "knowledge" that your particle and the E.
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