Distance, Displacement, Speed, Velocity and Acceleration – Best Notes for competitive exams

This post is about the definition, units and dimensions of distance, displacement, speed, velocity, Acceleration, the difference between distance and displacement, and the difference between speed and velocity.

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Distance, Displacement, Speed, Velocity and Acceleration

Distance-

Distance is the length of the actual path covered by a moving object in a given time interval.

Units of Distance-

• SI unit of distance is metre (m)
• CGS unit of distance is centimetre (cm)

But in our daily life, we come across the bigger units of distance e.g. kilometer.

The dimensional formula for distance- [M⁰LT⁰ ]

Characteristics of distance :

1. Distance is a scalar quantity.
2. Distance travelled by a body in a given interval of time is always positive.
3. Distance travelled by vehicles is measured by a device ODOMETER, fitted on the dash board of vehicles.
4. It can never be zero or negative.

Displacement-

It is the shortest distance travelled by the object between the initial to final positions of the object.

Units of Displacement-

• SI unit of displacement is metre (m)
• CGS unit of displacement is a centimetre (cm)

The dimensional formula for displacement is [M⁰LT⁰]

Displacement of an object in motion can be positive, negative or zero.

Characteristics of displacement-

1. Displacement has the unit of length.
2. Displacement of any object in a given interval of time may be positive, negative or zero.
3. Displacement of any object is a vector quantity as it has both magnitude and direction.
4. Displacement of any object is the shortest path between two positions.

Difference between Distance and Displacement

Distance	Displacement
1. It is the actual path travelled by object.	1. It is the shortest path travelled by the object between initial to final position.
2. Distance is the scalar quantity.	2. Displacement is the vector quantity.
3. Distance travelled by the object is always positive.	3. Displacement of the object in given interval of time may be positive, negative or zero.
4. Distance travelled by the object depends on the shape of the path followed by object.	4. Displacement is independent of the path followed by the object between initial and final position.

Speed

The speed of any object in motion is the ratio of the total path length (distance) and corresponding time taken by the object i.e,

Speed = Total distance / Time taken

Speed is a scalar quantity as it has only magnitude but no direction.

Speed of object gives no idea about the direction of motion of object. It may be positive and zero but never negative.

Unit of Speed-

In the SI system, the unit of speed is m/s and in the CGS system of the unit of speed is cm/s.

Speed of vehicles like car, bus etc. is expressed in km/h

Dimension formula of speed [M⁰LT^-1]

Velocity

The rate of change of displacement with respect to time is called velocity.

Velocity = Displacement / Time

Unit of Velocity

SI unit of velocity is m/s and CGS unit of velocity is cm/s

It is also expressed in km/h.

Dimension formula of Velocity [M⁰LT^-1]

Characteristics of Velocity-

• As velocity has both magnitude and direction so, it is a vector quantity.
• The velocity of an object can be positive, negative or zero according to displacement which can be positive, negative or zero.

Difference between Speed and Velocity

Speed	Velocity
1. Speed of a body is the distance travelled by it per unit of time.	1. Velocity of a body is the displacement of the body per unit of time.
2. Speed is a scalar quantity.	2. Velocity is a vector quantity.
3. Speed of a body is always positive.	3. Velocity of a body may be positive, negative, or zero.
4. Speed tells nothing about the direction of motion of the body.	4. Velocity tells about the direction of motion of the body.

Acceleration

Acceleration is defined as the rate of change of velocity with respect to time. Also defined as the change in velocity of object in unit time.

Acceleration = Change in velocity / Time

Acceleration is a vector quantity. Its direction is same as that of change in velocity.

SI unit of acceleration = m/s²

CGS unit of acceleration = cm/s²

Dimensional formula of acceleration = [M°LT^-2]

Acceleration of the object is positive if the velocity is increasing and is negative if the velocity is decreasing.

The negative acceleration is also called as Retardation or Deceleration.

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