Short Answer:

Displacement, velocity, and acceleration are the three important terms used to describe the motion of a body. Displacement is the shortest distance between the initial and final position of a moving object in a specific direction. Velocity is the rate of change of displacement with respect to time and includes both magnitude and direction. Acceleration is the rate at which velocity changes with time. These quantities help in understanding how fast and in what direction an object is moving or changing its motion.

In simple words, displacement tells how far and in which direction an object has moved, velocity tells how quickly it is moving, and acceleration tells how quickly the speed or velocity is changing. All three are vector quantities and have both magnitude and direction. They are the basic concepts in the study of motion in mechanics.

Detailed Explanation :

Displacement

Displacement is defined as the shortest distance between the initial and final position of a moving object in a particular direction. It is a vector quantity, which means it has both magnitude and direction.
If a body starts from a point and comes back to the same point after moving, its displacement becomes zero because the initial and final positions are the same, even though the distance covered is not zero.

Formula:

where,
= initial position,
= final position.

Unit: meter (m) in SI system.
Nature: Vector quantity.

Example:
If a car moves 5 m east and then 5 m west, the total distance covered is 10 m but the displacement is 0 m, because it returns to its starting point.

Thus, displacement helps to find the net change in position of a body, not the total path length.

Velocity

Velocity is the rate of change of displacement with respect to time. It tells how fast an object is moving and in which direction. Since it depends on displacement, velocity is also a vector quantity.

Formula:

Unit: meter per second (m/s).
Nature: Vector quantity.

Velocity can be of two types:

1. Average Velocity: It is the total displacement divided by total time taken.

1. Instantaneous Velocity: It is the velocity of a body at a particular instant of time.

Example:
If a train moves 100 m east in 10 seconds, then

If the direction changes, the velocity also changes, even if the speed remains constant. Therefore, velocity considers both magnitude and direction of motion.

Acceleration

Acceleration is the rate of change of velocity with respect to time. It tells how quickly the velocity of a moving body increases or decreases. Acceleration is also a vector quantity because it has direction.

Formula:

where,
= initial velocity,
= final velocity,
= time taken for the change.

Unit: meter per second square (m/s²).
Nature: Vector quantity.

If acceleration is positive, the body speeds up; if negative, it slows down (called deceleration or retardation).

Example:
If a car increases its velocity from 10 m/s to 30 m/s in 5 seconds,

It means the car gains 4 meters per second in velocity every second.

Acceleration plays an important role in mechanics as it determines how force and motion are related. According to Newton’s Second Law of Motion,

which shows that acceleration is directly proportional to the applied force and inversely proportional to mass.

Relationship Between Displacement, Velocity, and Acceleration

All three quantities are interrelated in motion. Displacement shows the change in position, velocity shows the rate of this change, and acceleration shows how the velocity itself changes over time.
The mathematical relationships among them are:

and

These equations form the foundation of kinematics, which deals with the motion of bodies without considering the forces that cause them.

Practical Example

Consider a ball rolling down a slope.

• Its displacement is the straight line from its starting point to where it stops.
• Its velocity keeps increasing as it moves down due to gravity.
• Its acceleration is constant if the slope is uniform.

Such simple examples help visualize how these three quantities are connected in real-life motion.

Conclusion

Displacement, velocity, and acceleration are the basic and essential quantities used to describe motion. Displacement measures the change in position, velocity measures the rate and direction of that change, and acceleration measures how the velocity varies with time. Understanding these concepts helps in studying the motion of objects in both straight and curved paths. They form the base of all topics in mechanics and are widely used in engineering calculations, physics problems, and real-world applications like vehicles, projectiles, and machinery motion.