Acceleration is known as the rate of change of velocity because velocity is a vector quantity that includes direction and speed. Acceleration is the rate at which the velocity changes over time, including changes in speed and/or direction. Here's why:

Velocity vs. Speed

- Velocity is a vector quantity that includes both speed and direction. For example, a car traveling at 60 km/h north has a different velocity than a car traveling at 60 km/h south.
- Speed is a scalar quantity that only refers to how fast an object is moving, regardless of direction. For example, a car traveling at 60 km/h north has the same speed as a car traveling at 60 km/h south.

Rate of Change of Velocity vs. Speed

- Acceleration is the rate of change of velocity, which means it includes changes in both speed and direction. For example, a car accelerating from 0 km/h to 60 km/h north is changing its velocity because it is changing its speed and direction.
- If acceleration were the rate of change of speed, it would only refer to changes in how fast an object is moving, regardless of direction. For example, a car accelerating from 0 km/h to 60 km/h north would have the same acceleration as a car accelerating from 0 km/h to 60 km/h south, even though they are changing their velocities in different directions.

Conclusion

In summary, acceleration is known as the rate of change of velocity because it includes changes in both speed and direction. Velocity is a vector quantity that includes both speed and direction, while speed is a scalar quantity that only refers to how fast an object is moving, regardless of direction.

It is becoz speed and velocity differs from each other .. Acceleration includes direction so it is said that rate of change of velocity as velocity is speed in a particular direction while speed has no definite direction.