Lesson 8: Average Speed and Instantaneous Speed; and Average Velocity and Instantaneous Velocity
Video Lesson
Lesson Objective
Dear Learners,
By the end of this section, you should be able to:
- Differentiate between average speed and instantaneous speed;
- Compute the average speed of a body; moving in a straight line covering a certain distance in a given time;
- Estimate the speed of moving bodies in your surroundings.
- Differentiate between average velocity and instantaneous velocity;
- Compute the average velocity of a body moving in straight line covering a certain displacement in a given time.
Brainstorming Question
Does the average speed the same as the magnitude of the average velocity?
Key terms and concepts
- Speed
- Velocity
- Average velocity
- Instantaneous velocity
Speed is the rate of change of distance.
Velocity is the rate of change of displacement.
Average velocity is the total displacement of a body over a time interval.
Instantaneous velocity is the velocity of a body at a specific instant in time.
Average Speed
Average speed is defined as the total distance travelled divided by the total time taken to travel that distance. It gives a measure of how fast an object is moving over a period of time, without regard to variations in speed during the journey. It is a scalar quantity, meaning it only has magnitude and no direction. Mathematically the average speed is given:
Average Speed=Total Distance /Total Time
v av = stot / ttot
The SI unit of average speed is m/s.
Example:
If a car travels 150 kilometers in 3 hours, the average speed is:
Solution:
Average Speed=150 km/3 hr=50 km/hr.
Instantaneous Speed
Video Cars speedometer
Instantaneous speed is the speed of an object at a specific moment in time. It can be measured using a speedometer or calculated as the limit of the average speed as the time interval approaches zero. It is also a scalar quantity. It reflects any changes in speed due to acceleration or deceleration. Mathematically the instantaneous speed is given:
v ins= ∆s/ ∆t as ∆t → 0
Where, ∆s is the distance travelled during the given very short time interval ∆t. Instantaneous speed and average speed are both scalar quantities. The SI unit of instantaneous speed is m/s.
Speedometer.
Example:
- A car’s speedometer showing 60 km/hr at a particular moment gives the instantaneous speed of the car at that moment.
Simulation (Average velocity and instantaneous velocity)
Average Velocity
Average velocity is defined as the total displacement divided by the total time taken for that displacement. It is a vector quantity, meaning it has both magnitude and direction. It gives information about the overall change in position over time but does not provide details about variations in speed or direction during the journey. Mathematically the average velocity is give
Average Velocity=Total Displacement/Total Time
V = S/t
The SI unit of average velocity is m/s.
Example:
- If a person walks 5 kilometers east in 2 hours, then turns around and walks 3 kilometers west in 1 hour, the total displacement is 2 kilometers east, and the total time is 3 hours:
solution:
Average Velocity=2 km east / 3 hr=32 km/hr east
Instantaneous Velocity
Instantaneous velocity is the velocity of an object at a specific moment in time. It is also a vector quantity. It indicates both the speed and the direction of the object at that particular instant. It reflects changes in speed and direction due to acceleration or deceleration. Mathematically the instantaneous velocity is given:
v ins= ∆s/ ∆t as ∆t → 0
Where, v ins is Instantaneous velocity, ∆s is the displacement travelled during the given very short time interval ∆t. The SI unit of instantaneous velocity is m/s.
Example:
- If a car’s velocity at a specific instant is 60 km/hr north, this means the car is moving north at a speed of 60 km/hr at that precise moment.