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.

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 = \[\frac{Displacement}{Time\:Taken}\]

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 |

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.

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)

Instantaneous Speed = limit as a change in time approaches zero (change in positron/ change in time)

v = lim_{Î”t}_{â†’}_{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:

**Difference between average speed and instantaneous speed:**

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 |

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. |

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 = lim_{Î”t}_{â†’}_{0}_{ } = \[\frac{\Delta s}{\Delta t}=\frac{\Delta s}{\Delta t}\]

Where dS is the displacement vector.

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. |