# Instantaneous Speed and Velocity

## Difference Between Instantaneous Speed and Velocity

Velocity and Speed:

Velocity and speed are related to displacement and distance respectively. Speed is the distance per unit time and velocity is the displacement per unit time. Speed has magnitude but no direction i.e. scalar similar to distance. Velocity has magnitude with direction i.e. vector similar to displacement.

Formulas for speed and velocity:

Speed = rate of change of distance = $\frac{Change\:in\: Distance}{Change\: in\: Time}$

Velocity = rate of change of displacement = $\frac{Change\:in\:Displacement}{Change\:on\:Time}$

Similar to distance and displacement which have distinctly different meanings regardless of their similarities, speed and velocity also have different meanings. A body/ object that moves with a high speed can cover a large distance within a short period of time. Contrast to that will be the distance covered and time taken for an object/ body that moves with low speed. An object with no movement will have a zero speed.

For instance, a person who is moving rapidly- one step forward and one step backward, it means that he returns to his starting position. This will result in a zero velocity. The motion will never result in a change of position since the person always tends to return to his original starting point. In order to maximize the velocity, a person in motion must maximize the distance that he is displaced from the original position.

Average speed and average velocity:

A moving body/ object often undergoes changes. Average speed is the distance traveled by the object divided by the time taken for the travel.

Average speed = $\frac{Distance\: Traveled}{Time \:of \:Travel}$

Whereas, average velocity is the changes in the position i.e. the displacement divided by the time taken.

Average velocity = $\frac{Displacement}{Time\:Taken}$

Difference between average velocity and average speed:

 Criteria Average velocity Average speed Meaning The change in the displacement i.e. the position divided by the time taken The distance traveled by the object divided by the time taken Formula Displacement/ Time taken Distance traveled/ Time of travel Sign It can be either positive or negative It will always be positive Measurement in unit m/ s m/ s Scalar or vector Vector Scalar

Instantaneous Speed:

The rate of change of position with time is called speed. As an object moves, its speed may change accordingly. The speed of an object at any given instant is called an instantaneous speed. It can be determined by finding out the average speed over a very short distance and time.

The formula for Instantaneous speed:

It is equal to the speed at an interval of time. Following is the formula for finding out the instantaneous speed:
Instantaneous Speed = limit as a change in time approaches zero (change in positron/ change in time)

v = limÎ”tâ†’0 = $\frac{\Delta x}{\Delta t}=\frac{\Delta x}{\Delta t}$

Here, x is the distance traveled by the body. The Instantaneous Speed is measured in meter per second (m/ s) as it is the speed at a particular time interval.

Both the instantaneous speed and velocity will be present in a moving object. The distance traveled with respect to time is the scalar quantity and how fast an object is moved is shown by this.

For example:

A school bus undergoes changes in speed. Speedometer will show the changes in speed for a regular interval of time.

Speed for various objects is given below:
 Objects m/ s m/ h Brisk walk 1.7 3.9 Sprint runner 12.2 27 Official land speed record 341.1 763 Space shuttle on reetry 7800 17,500 The speed of sound at sea level 343 768

Difference between average speed and instantaneous speed:

 Average speed Instantaneous speed The total distance covered by an object during a certain time span is used to calculate the average speed. The exact speed that an object at motion at a given instant time is the instantaneous speed.

Instantaneous Velocity:

Velocity at a specific instant in time is the instantaneous velocity. If the velocity is not constant, then it will differ from that of the average velocity. At the same time, for an object with standard velocity over a period of time, its instantaneous velocity and average velocity will be the same. The calculation for instantaneous velocity at a particular moment is done by substituting the corresponding time value of a variable, in the first-time derivative of the displacement equation.

Instantaneous velocity = v = limÎ”tâ†’0 = $\frac{\Delta s}{\Delta t}=\frac{\Delta s}{\Delta t}$

Where dS is the displacement vector.

Difference between average velocity and instantaneous velocity:

 Average velocity Instantaneous velocity In order to find an average velocity for an object, divide its total displacement by the total time taken for an object to move from one place to the other. The velocity of an object at a single instant in time is the Instantaneous velocity.