A key area of discussion in physics is velocity. A body’s velocity affects various properties, including kinetic energy and viscosity. We use the term velocity when describing how rapidly or slowly an item travels. The pace at which an object’s location changes concerning time and frame of reference is known as its velocity.
The concept of velocity is frequently used in fields as diverse as kinematics, kinetics, dynamics, astronomy, and engineering. It is essential to have a solid understanding of average and instantaneous velocity concepts to succeed in such fields.
What is Instantaneous Velocity?
The pace at which an item moves over time is known as its velocity. Said velocity is the rate of movement in a certain direction. Instantaneous velocity is the speed that is specified at a specific time. The instantaneous velocity formula, which we’ll explore later in this session. It can provide a more detailed description of instantaneous velocity.
Maintaining the speed limit is crucial when operating a vehicle. Even if the idea of instantaneous velocity may seem obvious, it is important to consider an illustration. Drivers refer to speedometers to keep track of a car’s instantaneous velocity. As a result, the car’s instantaneous velocity is higher than the law allows. Therefore the driver must slow down to stay within the legal limit.
What is Average and Instantaneous Velocity?
The speed of an item in motion at a certain moment in time is known as its instantaneous velocity. In this article, we conduct hands-on research to collect information enabling a quantitative, in-person examination of instantaneous and average velocity. Moreover, the Preliminary Physics course’s Kinematics and Motion in a Straight Line modules provide data visualisation and interpretation.
Dividing the displacement by the whole time required yields the average velocity, a vector quantity. The definitions of instantaneous and average velocity are covered in further detail in the next two movies about motion. The second video provides a more comprehensive explanation of instantaneous speed and velocity. In contrast, the video on motion is very helpful in comprehending more aspects of motion in a straight line.
Instantaneous Velocity Formula
Let’s say a particle moves in a way that allows it to go different distances at equal periods. The speed is therefore described as changeable, and the instantaneous speed is the speed at a certain moment. An automobile’s speedometer displays the vehicle’s current speed. A particle may also move at different speeds. A change in magnitude, direction or both can affect velocity.
If this is the case, we must attempt to ascertain the instantaneous velocity, which is the particle’s velocity at any given time. The following equation may be used to calculate the instantaneous velocity from the average velocity. The average particle velocity for smaller and smaller time intervals will be known from this formula if we keep reducing the period.
Instantaneous Velocity = LimΔT → 0 ΔS/ΔT = dS/dT
The formula above will allow us to determine the particle’s velocity at a certain point in time when it is infinitesimally tiny. The displacement vector, therefore, approaches a limiting direction, namely that of the tangent to the particle’s journey at that moment, if we let delta t – 0. As a result, the instantaneous velocity vector’s orientation is always perpendicular to the particle’s track. The magnitude of the velocity vector may be used to define the instantaneous speed.
Instantaneous Velocity vs. Instantaneous Speed
Typically, we swap “velocity” with “speed,” as shown in the example above. It’s crucial to tell them apart. Whereas instantaneous speed is a scalar number, the instantaneous velocity is a vector quantity. A scalar quantity has a magnitude, but a vector quantity has both a magnitude and a direction.
This implies that 50 mph east and west have different velocities while traveling simultaneously. The size of instantaneous velocity is known as instantaneous speed. The direction of the displacement is typically understood from the surrounding circumstances. The speed is employed as a shorthand for the velocity, for example, 50 mph vs. 50 mph “east.” To be cautious, the statement of the instantaneous velocity should include the direction of the displacement.
Instantaneous Velocity Equation
As the tiny limit of the equation for average velocity, we may now declare the defining equation for instantaneous velocity:
v = dx/dt
Where dt is a tiny unit of time and dx represents the object’s infinitesimal shift in location. The dimensions and units of these infinitesimal quantities are identical to those of their finite counterparts. As a result, dt is a time dimension and may be expressed in terms of seconds, hours, days, etc. At the same time, dx is a length dimension and can be expressed in meters, feet, miles, etc.
The displacement variable is significant since it is a vector and has direction. According to the velocity equation above, instantaneous velocity inherits the dimensionality of its defining variables. It can be measured in terms of meters per second, miles per hour, kilometers per hour, etc., and has dimensions of length over time. The instantaneous velocity is the slope of the line at that specific moment on a location versus time graph.
Equation of Motion
It is necessary to determine an object’s equation of motion to calculate its velocity at any given moment. The formal definition of velocity, a vector quantity, is the rate of change of position or displacement over time. Each vector, such as the speed of an object, has a direction and a magnitude. Speed and velocity are thus distinct concepts.
Velocity is a vector, whereas speed is a scalar. Speed is the magnitude of velocity to simplify things. We define velocity in terms of a predetermined frame of reference, and its unit is meters/second. Two methods may be used to measure it. The other is instantaneous velocity, whereas the first is average velocity.
The physical velocity of a body at a location is also known as the instantaneous velocity. Based on average velocity, we created the idea of instantaneous velocity and investigated its magnitude and direction. Even though we have looked at various viewpoints and expressions for the velocity vector and its magnitude. The velocity is often calculated as the position vector’s derivative concerning time.
Also read: Velocity Formulas in Translation and Circular Motion