Speed vs Velocity – Understanding their Difference

Kinematics and dynamics are fascinating areas of physics that help us understand how objects move. In these areas, two important concepts are "speed" and "velocity." Although they may seem similar, they have different meanings and applications. This lesson will explore the differences between speed and velocity in depth, and provide several examples to illustrate these concepts.

What is speed?

Speed is a scalar quantity, which means it has only magnitude and no direction. It tells how fast an object is moving regardless of its direction of travel. Basically, speed tells you how much distance an object has traveled in a specific time period.

The formula for calculating speed is:

Speed = Distance / Time

Where:

• Speed is usually measured in metres per second (m/s) or kilometres per hour (km/h).
• Distance is the total length of the path covered by the object.
• Time is the period during which the movement occurred.

For example, if a car travels 150 kilometers in 3 hours, then the speed of the car will be:

Speed = 150 km / 3 h = 50 km/h

It's important to note that speed doesn't tell you which direction the car is going, but how fast it's going.

Visual example of motion

In this example, a vehicle travels on a straight path covering a distance of 150 km from the starting point to the ending point. The speed does not give any other information about the path except the distance.

What is velocity?

Velocity is a vector quantity, which means it has both magnitude and direction. Velocity describes the movement of an object in a specific direction. Therefore, velocity gives more information about the motion of an object than speed.

The formula for calculating velocity is similar to that for speed, but it also includes direction:

Velocity = Displacement / Time

Where:

• Velocity is usually measured in metres per second (m/s) or kilometres per hour (km/h).
• Displacement is the straight line distance from the starting point to the final point in a particular direction.
• Time is the period during which the movement occurred.

Example of velocity

Imagine that a person walks 100 m east in 50 seconds. The velocity of that person will be:

Velocity = 100 meters east / 50 seconds = 2 m/s east

This example shows that velocity tells us not only how fast the person is moving, but also in which direction he is moving.

Visual example of velocity

In this scene the person moves in a specific direction (east), giving us information about both speed and direction - this is called velocity.

Main differences between speed and velocity

Now that we have a basic understanding of speed and velocity, let's outline the key differences between these two concepts.

1. Nature

• Speed is a scalar quantity. It only measures the magnitude of speed.
• Velocity is a vector quantity. It measures both the magnitude and direction of motion.

2. Direction

• Speed does not include direction. A speed of 60 km/h can mean any direction.
• Velocity also includes direction. A velocity of 60 km/h due north tells the direction in which the object is moving.

3. Calculation

• Speed is calculated based on the total distance travelled.
• Velocity is calculated using displacement, which is the shortest path between the initial and final points.

4. Practical understanding

• On a vehicle's speedometer you only see speed, which tells you how fast you're going at that moment, without giving you direction.
• Air traffic controllers need to know an aircraft's speed to manage its flight path, as both speed and direction are important.

Examples to illustrate speed vs velocity

Example 1

A bird flies 500 m north in 200 seconds, and then flies 500 m south in 200 seconds. What is the average speed and average velocity of the bird?

Average speed :

Total distance = 500 m north + 500 m south = 1000 meters 
Total time = 200 s + 200 s = 400 s 
Average Speed = Total distance / Total time 
Average Speed = 1000 m / 400 s = 2.5 m/s

Average velocity :

Displacement = 0 meters (since the bird returns to the starting point) 
Total time = 400 s 
Average Velocity = Displacement / Total time 
Average Velocity = 0 m / 400 s = 0 m/s

This example shows that although the bird flew at an average speed of 2.5 m/s, its average velocity is still 0 m/s because it arrived back where it started.

Example 2

A bike travels 10 m east in 2 seconds, then turns and travels 10 m west in 2 seconds.

pace :

Total distance = 10 m east + 10 m west = 20 meters 
Total time = 2 s + 2 s = 4 s 
Speed = Total distance / Total time 
Speed = 20 m / 4 s = 5 m/s

Velocity :

Displacement = 0 meters (since the bike returns to the starting point) 
Total time = 4 s 
Velocity = Displacement / Total time 
Velocity = 0 m / 4 s = 0 m/s

Again, even though the bicycle is moving at 5 m/s, the velocity is 0 m/s because it has returned to the starting point.

Summary

Understanding speed and velocity is important to understand how objects move. Speed is simple but lacks direction, while velocity provides a more detailed description by taking direction into account. Remember, both concepts are essential in physics, and understanding the difference helps to accurately analyze various motion scenarios.

Comments