 # Unit of Velocity  View Notes

## SI Unit and Other Velocity Units

The unit of velocity can be defined as the ratio of unit of distance and unit of time. Students should not confuse velocity with speed as both are different to one another. Although the unit of speed and unit of velocity are similar, velocity being a vector quantity is defined as the rate at which an object changes its position with respect to a frame of time and reference.

The unit of velocity and speed is m/s and the formula for average velocity is

V= s/t, where s is the displacement

t is the total time taken

Speed: Speed is a scalar quantity and is defined as the rate of change of position of an object in any position and time.

The formula for speed is

s = d/t, where s is the speed in m/s

d is the distance travelled

t is the total time taken

Distance: The length of the actual path traversed by the body during motion in a given interval of time is called the distance traveled by that body.

Distance is a scalar quantity and it can never be zero or negative during the motion of an object.

Displacement: At a given interval of time, the displacement is defined as the shortest distance between the two positions of the body in a particular direction at that time and is given by the vector traced from the initial position to the final position.

Displacement is a vector quantity i.e., it has both magnitude and direction. Therefore, in a given interval of time, it can be positive, zero, or negative.

 The SI unit of distance and displacement is meter, is denoted by m

### SI Unit of Velocity

The velocity of the body is defined as the rate of change of displacement of the body with time. It is also defined as the speed of an object in a given direction. The relation is given by,

 Velocity  = Displacement / Time

Velocity is a vector quantity i.e.,  it has both magnitude (speed) and direction.

The velocity depends upon the displacement of the object which means velocity can be zero, positive, or negative according to its displacement as zero, positive or negative.

SI  unit or  MKS (Meter-kilogram-second) unit of velocity is also meter per second or m/s or m s⁻¹ where m/s is the SI base unit of velocity.

### Velocity Unit Symbol

The symbol for the unit of velocity is ms⁻¹ or m/s.

### SI unit of Average Velocity

The average velocity of the object is defined as the total  displacement of the object divided by the total time taken. It is given by,

 Average velocity = Total displacement/ Total time taken

The SI unit of average velocity is ms^ -1 or m/s.

The dimensional formula for the same is given by [M L T ^ -1]

CGS(centimeter-gram-second) unit for velocity is cm s⁻¹ .

### The SI Unit of Speed Is

Speed of an object is defined as the rate of change of position of an object in any direction. It is given by,

 Speed = distance traveled/time taken

Speed is a scalar quantity. It gives no idea about the direction. However, the speed of the object can be positive, zero, or negative.

 The SI or MKS unit for the speed is m/s or ms⁻¹  The CGS (centimeter-gram-second) unit for the speed is centimeter per second or cm s⁻¹ or cm/s.

Angular Velocity Units

The angular velocity of an object in a circular motion is specified as the rate of change of its angular displacement. It is usually represented by the symbol omega (ω) given by,

 ω  = angle traced/ time taken =  limit Δ Ө / Δ t =   d Ө/ dt                                                    Δt -> 0

Angular displacement is a vector quantity. Its direction is the same as that of  Δ Ө.

Where ΔӨ is the angular displacement and is defined as an angle made by an object moving around a circular path.

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: [M⁰ L⁰ T⁻¹]

### Angular Displacement Units

The angular displacement of the object moving around a circular path is defined as the angle made or traced by the radius vector at the axis of the circular path in a given time.

 Where angle (Ө) = arc / radius (r)

Such as the motion of a stone when tied to a string makes an angle Ө where Ө  is the angle swept by the stone.

Angular displacement is a vector quantity.

 The unit of angular displacement is the radian

### Unit of Velocity of Light

The velocity of light is a fundamental constant that corresponds to the speed of an electromagnetic radiation in a vacuum and has a value approximately equal to 2.9979 x 10¹⁰ centimeters per second.

The unit of velocity of light is taken as the unit of velocity i.e., SI or MKS unit is m/s and CGS unit is cm/ s.

### Velocity Units

• Miles per hour (mph)

• Kilometers per hour (kmph)

• Knot

• Foot per second or ft /s or fps

• Feet per minute or ft/ m or fpm

• Foot per hour

• Meter per hour

• Inch per second

• 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

• Speed of light

• Benz (Bz)

1. What is the Difference Between Velocity and Relative Velocity?

Ans: The difference between velocity and relative velocity is,

• Velocity is the speed at which an object moves in a direction is measured with respect to a frame of reference that is relative to different points.

• Relative velocity is defined as the rate of change of relative position of one object with respect to another and is measured in a frame where the object is either at rest or moving with respect to the absolute frame.

2. Can Velocity be Positive or Negative? State with Example.

Ans: Since velocity is a vector quantity i.e., it has a direction.

For example, when I’m driving towards my office,  then my velocity is positive and when I am driving towards home from office then the velocity is negative as the direction of the moment is opposite,  then my velocity would be negative. However, negative velocity doesn’t exist practically, it’s all about the direction we consider.

Hence, negative velocity implies the velocity in the opposite direction than what would be positive.

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