The concept of velocity has been around for centuries. Velocity is the rate at which something changes position, specifically how fast something moves from one position to the next.
However, in physics velocity is defined as the rate at which an object changes its position with respect to time. This is a very specific definition of velocity that requires the use of the term “with respect to time.”
How can one define velocity without the requirement of time? How can one determine how fast something moves from one position to the next if time is not a factor? These are questions that will be answered in this article.
Velocity, as defined in physics, is a vector quantity. This means that it has both a magnitude (or size) and a direction. The length of the vector represents the magnitude of the velocity, and the direction describes which way the object is moving.
Example of motion
In this example, the particle moves along a straight line such that its position is defined by S=(t2−6t+5) M.
This equation is a function that describes the position of the particle as a function of time. A function is just a recipe for combining inputs (in this case, time) to get an output (position).
We can analyze this equation in two ways: graphically and numerically. Let’s do both!
Graphical analysis: The first thing we will note is that the graph of this function is a straight line with slope 2 and y-intercept 5. This means that if we draw the graph of S=x, then x=5 and x2=2. Additionally, since it is a straight line, any value of time will give us the same value of position.
Numerical analysis: Now let’s do some numerical analysis to see what interesting properties arise from this function. If we consider two different cases—when t=1 and when t=infinity—we see some interesting properties emerge.
Properties of motion
Motion can be described in terms of velocity, acceleration, and position. Velocity is how fast an object moves, acceleration is how fast its speed changes, and position is where it is.
Velocity is a measurement of speed so it does not account for the object’s direction. Acceleration does account for the object’s direction and change in direction.
These properties of motion are related by the laws of physics. The more detailed laws describe precisely how each property changes as a result of a specific kind of acceleration or change in velocity.
For example, the laws of physics state that velocity changes as a result of acceleration, so if there is a constant acceleration then the velocity changes by being constant. The law also states that if the acceleration changes then the velocity changes by being non-constant.
There are many different types of motion, all of which are described on this page.
Constant speed
Constant speed motion is a bit more complicated than straight-line motion. In this case, the particle moves along a straight line such that its velocity is constant.
Constant speed motion is when a particle moves at a constant speed for some extended period of time. This can be described by two variables: velocity and displacement.
Velocity is the average speed that the particle moves along its path. Displacement is how far the particle moves during this time period.
In constant speed motion, the velocity and displacement are not related. The only thing that connects these two variables is that both are what define the path of the particle.
It is important to note that in constant speed motion, the average velocity does not change over time. A good way to think about this is water moving across a flat surface. The flow of water does not change, so its average velocity does not change.
Linear velocity
Linear velocity is the rate at which a position changes with respect to time. In other words, it describes how far a particle moves per unit of time.
Velocity is defined as the ratio of displacement to time period. Thus, velocity can be expressed as:
where:
is the velocity, is the displacement between two points in space, and is the time period between two points in time.
Linear velocity can be negative or positive, with negative velocities being equivalent to backwards linear motion. Positive linear velocities are equivalent to forward linear motion.
This can be further explained through the use of derivatives, which define a constant rate of change. A derivative can be either positive or negative, meaning that it can describe either increasing or decreasing rates of change.
Position equation
A particle moves along a straight line such that its position is defined by S=(t2−6t+5) m, where t is time and m is the magnitude of the velocity. This equation is called the position equation.
Velocity is how fast a particle moves in a given direction, so to find its velocity you need to solve for v in the velocity formula: v=s/t.
So, if we replace s with S in the above position equation, we get v=v2−6v+5, where v2=v·v and v=m/t. This shows you that the vector velocity is always perpendicular to the direction of motion (in this case, the straight line).
You can also use the velocity formula to find how long it takes for a particle to travel a certain distance. If you set t=0 in the above formula, you get V2−6V+5=0, so V=(−6±5)V2, or V=(−6±5)m/s.v1 = velocity 1 = Velocity at A
Since point A is on a curve and not on a straight line, this point has both a position (xA) and a vector displacement (xa). To calculate xA you must first find xa using the radius of curvature r and then subtract xa from xA.
To find radius of curvature r: r = [length around curve] / [length across curve]
To calculate xA-xa: xA-xa = [Position at A] – [Position at end of arc]
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Jarrett wrote this article., Dec 19 2017 6:00am EST
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Initial position value
The initial position of a particle can be defined in several ways. The most common is the position at a certain time t=0.
Other methods include the position at a certain distance, or the position at a certain velocity. All of these can be transformed into a 0 as the time, distance, or velocity at which they are defined.
A particle moving with constant speed along a straight line such that its velocity is defined by V=(t2−6t+5) M per second has constant speed and therefore constant acceleration. Its position S=(t2−6t+5) M is also constant, since it is defined by its initial position at t=0.
This article will focus on the particle’s initial position at t=0, as this is most commonly studied in physics courses.
Final position value
The final position value of a particle is the position value when the particle has stopped moving. This is determined by the last time the particle’s velocity is updated.
The final position value is found by taking the last velocity value and applying it to an imaginary line that goes from the origin to infinity. The particle then sits on this line until it has stopped moving.
Particles do not actually move along a straight line such that their position is defined by S=(t2−6t+5) M., but this formula can be applied to an imaginary line that goes from the origin to infinity, where S=(t2−6t+5) M. stands for Simple Moving Average. The average moves along a straight line such that its position is defined by Simple Moving Average.
Time period
The time period is related to the frequency and wavelength of a particle wave. As mentioned before, frequency is the number of cycles per second, and wavelength is the distance between one cycle peak to the next.
The time period is the length of time it takes a particle wave to complete one full cycle. This is expressed in seconds, just like frequency and wavelength are.
We can calculate the time period using these variables, however only one of them needs to be known if we already know the other. The equation looks like this: T=1/f or T=λ/c where c is the speed of light in a vacuum.
Time periods can be very short depending on what particle we are observing and what its characteristic length (lambda) is. For example, if we are observing an electron moving at very high speeds, its time period will be very short due to its high frequency.
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