# Unit of Velocity

## Definition

The rate of change of displacement concerning time is known as velocity. In simpler terms, the ratio of displacement with time is known as velocity. It is a vector quantity, i.e., it has both magnitude and direction.

Displacement – The shortest distance between two objects or places is known as displacement. It is a vector quantity, which means displacement has both direction and magnitude. It is measured in meters or units of meters.

Speed is different from velocity. The table lists the difference between speed and velocity-

## Quantities dependent on velocity

 Speed Velocity It is the rate of distance. It is the rate of change of displacement. It is a scalar quantity. It is a vector quantity. It can never be zero or negative. It can be zero or negative. It may or may not be equal to velocity. A body may possess different velocities but the speed will remain the same. Speed never decreases with time. For a moving body, it can never be zero. Velocity can decrease with time. For a moving body, it can be zero.

The following quantities depend upon velocity and may use its units to derive their own-
1. Kinetic energy
2. Acceleration
3. Momentum
4. Escape velocity
5. Gravitational acceleration

## SI unit

Velocity = displacement / time = v/t
The unit of displacement is meters and time is seconds.
Therefore, the SI unit of velocity is m/s (can be written as ms-1)
The unit can also be cm/min or km/hr, depending upon the way it has to be expressed.
The dimensional formula for velocity is LT−1.

## Average velocity

Average velocity is defined as the ratio of total displacement upon total time taken by the object.
Average velocity = total displacement / total time
The SI unit of average velocity is the same as that of the velocity. Also, its dimensional formula is the same.

## Unit of velocity of light

Light belongs to a specific region in the electromagnetic spectrum. The velocity of light is a fundamental constant and has a value equal to 3 x 10¹⁰ centimeters per second. The unit of velocity of light is the same as the unit of velocity. It can be expressed in m/s, km/hr, etc.

## Angular velocity

The angular velocity is defined as the velocity of an object undergoing a circular motion. It is defined as the rate of change of the angular displacement. It is represented by omega ω. Angular velocity is a vector quantity. Its direction is the same as the angular displacement.
ω = angle traced/ time taken = limit Δ Ө / Δ t = d Ө/ dt, where Δt -> 0

The SI unit of angular velocity is radians per second.
Where radian is a dimensionless quantity.
The SI unit of angular velocity is 1/ s or second⁻¹ or s⁻¹.
In S.I. base units: s⁻¹.
The dimensional formula for angular velocity: M⁰L⁰T⁻¹M⁰L⁰T⁻¹

## Angular displacement

The angle made by the path traced by an object in the circular motion is known as displacement.

Angular displacement (Ө) = arc / radius
The unit of angular displacement is radian, which is a dimensionless unit.

## Other units of velocity

Some other units of velocity include-

• Kilometers per hour (km/hr)
• Knot (unit)
• Meter per hour (m/hr)
• Miles per hour
• Inch per second
• Speed of light
• Foot per second or ft /s or fps
• Feet per minute or ft/ m or fpm
• Foot per hour
• Kilometers per second (kps)
• Centimeters per hour (cmph)
• Meter per minute
• Millimeter per minute (mmpm)
• Mile per minute
• Millimeter per second (mps)
• Centimeter per minute
• Benz (Bz)

## Example 1

An object travelled a distance of 10 meters in the left direction and the time taken by the object is 2 minutes. Find the velocity of the object.

Solution
We know, velocity = displacement ÷ time
v = a / t
Let us change the units of time by doing appropriate conversions.
Time in seconds = time in minutes × number of seconds in a minute
ts = 2 × 60 = 120 s
So, time in seconds is 120 s
v = 10 / 120
v = 0.08 m/s
The velocity of the object is 0.08 m/s.

## Example 2

A car is traveling in a circular path or track, and it travels 1 lap or 2π radians in 4 minutes. Then calculate the angular velocity of the car.

Solution:We know,
w = θ / t
w = 2pi / 4 = pi / 2
So, the angular velocity of the race car is pi / 2 radians per minute.

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