Instantaneous Velocity:

- Instantaneous velocity refers to the velocity of an object at a specific instant of time.
- It is a vector quantity that includes both the magnitude and direction of the velocity.
- It is calculated by finding the derivative of the position function with respect to time.
- The formula for instantaneous velocity is given as v = lim Δt → 0 (Δx/Δt), where Δx represents the change in distance and Δt represents the change in time.
- It is expressed in units of distance/time, such as meters per second (m/s) or kilometers per hour (km/h).
- Instantaneous velocity can be positive or negative, depending on the direction of the motion.
- It is a more accurate measure of an object's motion than average velocity or average speed because it takes into account the changes in velocity that occur over very small time intervals.

Instantaneous Speed:

- Instantaneous speed refers to the speed of an object at a specific instant of time.
- It is a scalar quantity that only includes the magnitude of the velocity, not the direction.
- It is calculated by dividing the distance traveled by the time taken to travel that distance.
- The formula for instantaneous speed is given as s = lim Δt → 0 (Δx/Δt), where Δx represents the change in distance and Δt represents the change in time.
- It is expressed in units of distance/time, such as meters per second (m/s) or kilometers per hour (km/h).
- Instantaneous speed can be positive or zero, but it cannot be negative because speed is always a positive quantity.
- It is a less accurate measure of an object's motion than instantaneous velocity because it does not take into account the changes in direction that may occur over very small time intervals.

Average Velocity:

- Average velocity refers to the average rate of change of an object's position over a given time interval.
- It is a vector quantity that includes both the magnitude and direction of the velocity.
- It is calculated by dividing the change in position by the change in time.
- The formula for average velocity is given as v = Δx/Δt, where Δx represents the change in distance and Δt represents the change in time.
- It is expressed in units of distance/time, such as meters per second (m/s) or kilometers per hour (km/h).
- Average velocity can be positive or negative, depending on the direction of the motion.
- It is a useful measure of an object's motion over a longer time interval, but it may not accurately reflect the object's motion at any particular instant.

Average Speed:

- Average speed refers to the average rate of change of an object's distance traveled over a given time interval.
- It is a scalar quantity that only includes the magnitude of the velocity, not the direction.
- It is calculated by dividing the total distance traveled by the time taken to travel that distance.
- The formula for average speed is given as s = total distance traveled/total time taken.
- It is expressed in units of distance/time, such as meters per second (m/s) or kilometers per hour (km/h).
- Average speed can be positive or zero, but it cannot be negative because speed is always a positive quantity.
- It is a useful measure of an object's motion over a longer time interval, but it may not accurately reflect the object's motion at any particular instant.