Table of contents:

What is velocity?

In its simplest term, velocity is the rate of change of displacement of an object w.r.t. time.

Table of contents:

We have already learnt that displacement is the overall change in position of an object that has travelled some distance.

Velocity is the rate of change of displacement of an object w.r.t. time. It has magnitude and direction, hence, it is a vector quantity.

What is speed then? It is the rate at which an object covers some distance. It is a scalar quantity; it has magnitude only, and no direction. It is simply the distance covered per unit time, i.e.,

speed = distance / time.

By the word speed we get an idea of how fast an object is moving. Velocity tells us how fast an object is changing its position alongwith the direction. It describes the speed of an object as well as the direction of movement.

Speed is calculated by dividing distance by time; velocity is calculated by dividing the actual displacement by time. Velocity is related with overall displacement of an object, speed is related with total distance covered by the object.

Scalar quantities:

A scalar quantity has only one property, magnitude. Speed is scalar, it has magnitude only.
We may ask "What is the speed of that car?"
and the answer may be 100 km/h.
"What is the area of a circle of radius 10cm?"
and the answer is 314 cm2 .

✫ Examples of scalar quantities are Speed, Area, Volume, Time etc.

Vector quantities :

On the other hand velocity is a vector quantity because it has two properties, magnitude & direction.
For velocity, our answer may be: 1000 km/hr north.

✫ Examples of vector quantities are Force, Momentum, Acceleration, Weight etc.

Observe the following animation.

Speed and Velocity A B 300m Total Time = 6s. Distance = 300m. Speed = (300 ÷ 6)m/s = 50 m/s Displacement = 300m. Velocity = (300 ÷ 6)m/s = 50 m/s (East) 0 1s 2s 3s 4s 5s 6s

In the above figure, a toy-car moves from point A to point B by 300 meters in 6 sec. Both the distance and displacement of the object are same in this case.

The following animation shows that distance and displacement of an object may be different.

Speed and Velocity A B C 300m 200m Total Time = 10s. Distance = (300 + 200)m. = 500m. Speed = (500 ÷ 10)m/s = 50 m/s Displacement = (300 - 200)m. = 100m. Velocity = (100 ÷ 10)m/s = 10 m/s (East) 0 1s 2s 3s 4s 5s 6s 7s 8s 9s 10s

In this case the car first moves 300m eastwards in 6 sec., and then 200m in reverse direction in another 4 sec.

A is initial position, C is final position
Time = (6 + 4) sec. = 10 sec.
Distance = 300m + 200m = 500m.
Displacement = 300m - 200m = 100m
∴ Speed = Distance÷Time = 50 m/s,
Velocity = Displacement÷Time = 10 m/s East

The SI unit of velocity is meters per second. In the following table, the main differences between speed and velocity have been laid out :

Differences between speed and velocity

Speed Velocity
Speed is scalar Velocity is vector
Related to distance travelled Related to total displacement & direction
Always positive May be positive, negative or zero

Displacement is either smaller or equal to distance. So velocity may be equal to speed in magnitude, or may be less. Both speed and velocity may take the same unit, such as m/s, Km/Hr. However for the latter, direction is important to mention, such as 900 km/hr East.

Different types of velocity

velocity-types'>Different types of velocity

When both magnitude and direction of velocity remain unchanged, it is known as uniform velocity.

Average velocity:

Divide total displacement of an object by total time taken to get average velocity, generally denoted by v   or   vaverage

Instantaneous velocity:

The velocity of an object at a particular point of the travel path is known as instantaneous velocity. The time duration must be too small to get accurate instantaneous velocity.

Initial velocity:

The velocity at the beginning of motion is known as initial velocity and is denoted by u   or   vi

Final velocity:

The velocity at the end of motion is called final velocity and is denoted by v   or   vf

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