Velocity - Definition, Example, Types, FAQs

What is Meant by Velocity?

Velocity is the rate of change of displacement with time. It tells us how fast and in which direction an object is moving.

In simple words, velocity is speed with direction.

$
\text { Velocity }=\frac{\text { Displacement }}{\text { Time }}
$

• Velocity is a vector quantity (it has both magnitude and direction).
• The SI unit of velocity is metre per second (m/s).
• If an object moves in a straight line without changing direction, its speed and velocity are the same.

Units of Velocity

Velocity is the rate of change of displacement with time, so its units depend on distance and time units.

Velocity Formula

The formula for velocity is:

$
\text { Velocity }(\mathrm{v})=\frac{\text { Displacement }(\mathrm{s})}{\text { Time }(\mathrm{t})}
$

Where:

• $\mathbf{v}=$ velocity
• $\mathbf{s}=$ displacement (change in position)
• $\mathbf{t}=$ time taken

Instantaneous Velocity Formula

Instantaneous velocity is the velocity of an object at a specific instant of time. It shows both the speed and direction of motion at that exact moment.

The formula is:

$
v=\frac{d s}{d t}
$

Where:

• $\mathbf{v}=$ instantaneous velocity
• $\mathbf{s}=$ displacement
• $\mathbf{t}=$ time
• $\mathbf{d s} / \mathbf{d t}=$ derivative of displacement with respect to time

Angular Velocity Formula

Angular velocity measures how fast an object rotates or revolves around a fixed axis. It tells us the angle rotated per unit time.

$
\omega=\frac{\theta}{t}
$

Where:

• $\omega=$ angular velocity
• $\theta=$ angular displacement (in radians)
• $t=$ time

SI Unit:

• radian per second (rad/s)

Relation with Linear Velocity:
If an object moves along a circular path of radius $r$,

$
v=\omega \cdot r
$

Where $v$ is the linear velocity.

Average Velocity Formula

Average velocity is the total displacement divided by the total time taken.

$
\text { Average Velocity }\left(v \_ \text {avg }\right)=\frac{\operatorname{Total} \text { Displacement }(\Delta x)}{\operatorname{Total} \operatorname{Time}(\Delta t)}
$

Where:

• $v_{\text {avg }}=$ average velocity
• $\Delta x=$ total displacement
• $\Delta t=$ total time

Difference between speed and velocity

Example of Velocity

1. A car travels $\mathbf{1 0 0}$ metres east in $\mathbf{2 0}$ seconds.

$
\text { Velocity }=\frac{\text { Displacement }}{\text { Time }}=\frac{100 \mathrm{~m} \text { east }}{20 \mathrm{~s}}=5 \mathrm{~m} / \mathrm{s} \text { east }
$

2. A train moves 200 km north in 4 hours.

$
\text { Velocity }=\frac{200 \mathrm{~km} \text { north }}{4 \mathrm{~h}}=50 \mathrm{~km} / \mathrm{h} \text { north }
$

Applications of Velocity:

• Vehicles: Helps know how fast and in which direction cars, trains, or planes are moving.
• Sports: Used to measure athletes’ speed and direction in running, cycling, or swimming.
• Traffic: Helps plan travel time and control traffic.
• Navigation: Ships and airplanes use velocity to reach places correctly.
• Weather: Wind velocity is used to predict storms and weather.

Related Topics Link,

• Unit of Velocity
• Unit of Distance
• Difference Between Speed and Velocity
• Relative Velocity
• Measurement of Speed

Also check-

• NCERT Exemplar Class 11th Physics Solutions
• NCERT Exemplar Class 12th Physics Solutions
• NCERT Exemplar Solutions for All Subjects

NCERT Physics Notes:

• NCERT Notes Class 11th Physics
• NCERT Notes Class 12th Physics
• NCERT Notes For All Subject