Linear Velocity

Understanding any concept in physics involves decoding the definition of the terms associated. In the case of linear velocity, it thus becomes necessary to define linear and velocity individually. 

Linear velocity refers to the movement of an object along a straight line or a pre-defined axis. On the other hand, velocity implies the distance that a moving body travels in a specific direction within a particular time. Therefore, the combination of these two definitions will lead you to understand the basic concept of linear velocity. 

What is Linear Velocity? 

In the most primary sense, linear velocity definition deals with the measurement of an object’s velocity when it moves along a specific direction. Therefore, it refers to the displacement of an object with respect to time. 

However, the object has to follow a specific straight line in terms of its movement. The SI unit of linear velocity is meter per second or m/s (m s-1). 

On the other hand, the linear velocity dimensional formula is [M]0[L]1[T]-1. Also, you should know that it is a vector quantity, which indicates it has directional nature. 

What is the Formula for Linear Velocity? 

There are no points of differences between conventional velocity and linear velocity, since both are vector quantities. 

Therefore, the linear velocity formula is – 

ν = d/t

Consider the following table to understand what each of these signifiers stand for – 

[Table]

For instance, suppose that a moving object covers a distance of 500 meters along a straight line within 10 seconds. In that case, the linear velocity of the object is – 

ν = 500 meters/10 seconds = 50 m/s or 50 m s-1

Logically speaking, linear velocity also applies to an object that moves in a circular direction, following a locus. In that case, it is termed as angular velocity. 

What is Angular Velocity? 

Angular velocity is primarily the ratio of the angle that an object covers within a particular amount of time. In this instance, ϴ refers to the angular displacement at which a body rotates around a fixed axis. 

The formula expressing angular velocity is, therefore – 

νr = r.ω, 

Where νr refers to the angular velocity, ω implies time/radians, and r stands for the radius of the travelled path. Moreover, 2π radians equals to 3600 in this case. You should also know that every point of the object’s trajectory has the same angular velocity, because it remains constant throughout its journey. 

Can you Solve these Linear Velocity Problems?

  • Amrita runs in a single direction for 10 minutes at a constant velocity. She successfully covers 1.2 km from when she started running. What will be her linear velocity in SI units? 

  • The linear velocity of a specific car along a straight highway is 150 km/h, and it travels 50 km within a specific time. How much time (in seconds and minutes) will it take the car to cover that distance? 

  • A moving object X has a linear velocity of 100 m/s and travels from point A to B in 1 minute 40 seconds. What is the distance between point A and B? 

How does Linear Velocity Differ from Speed? 

Even though both velocity and speed aim to find out the distance that a moving object covers within a certain period, there are some points of differences between them.

First of all, speed is a scalar quantity. This suggests that the expression of speed in m/s or m s-1 conveys only the magnitude. It does not imply anything about the direction in which the moving object travels. Certain instances of scalar quantities are energy, mass, and time. 

On the other hand, linear velocity specifies the direction of travel. It is because velocity is a vector quantity and suggests both the magnitude and direction of the moving body. Some other examples of vector quantities are force and momentum. 

Now that you know what is linear velocity, make sure that you go through related topics to gather comprehensive knowledge on the same. Also, you can download our Vedantu app to benefit from our interactive learning experience from professionals in the field of physics. 

FAQ (Frequently Asked Questions)

1. What is Linear Velocity? 

Ans. Linear velocity is the rate of displacement when a moving object travels along a specific direction. 

2. What is the Formula for Linear Velocity? 

Ans. Linear velocity formula is ν = d/t, where v stands for velocity, d for displacement and t defines time.

3.  What is the Formula For Angular Velocity? 

Ans. Formula for angular velocity is νr = r.ω. , where νr stands for angular velocity, r for radius of its path and ω defines time/radians.