Calculating the Total Distance Moved

Oct 13, 2025 by wbrum.org 70 views

Introduction

When analyzing the motion of an object, it's essential to understand the concepts of distance and displacement. Distance refers to the total length of the path traveled by an object, while displacement is a measure of the object's change in position. In this article, we'll explore the motion of a hockey puck that moves 28 meters southward, then 14 meters northward, and finally 4 meters southward. We'll calculate the total distance moved and determine the magnitude and direction of the displacement.

Calculating the Total Distance Moved

To calculate the total distance moved, we need to add up the distances traveled in each direction. The hockey puck moves 28 meters southward, then 14 meters northward, and finally 4 meters southward. Since the puck moves in opposite directions, we need to subtract the distance traveled northward from the distance traveled southward.

Total distance = 28 m (southward) + 14 m (northward) - 4 m (southward)
Total distance = 34 m

Calculating the Magnitude and Direction of the Displacement

Displacement is a vector quantity, which means it has both magnitude and direction. To calculate the magnitude of the displacement, we need to find the net distance traveled in a single direction. Since the puck moves 28 meters southward and then 14 meters northward, the net distance traveled southward is:

Net distance southward = 28 m - 14 m
Net distance southward = 14 m

The puck then moves 4 meters southward, so the total displacement is:

Total displacement = 14 m + 4 m
Total displacement = 18 m

The direction of the displacement is southward, since the puck moves a net distance of 18 meters in that direction.

Conclusion

In conclusion, the total distance moved by the hockey puck is 34 meters, and the magnitude and direction of the displacement are 18 meters southward. Understanding the concepts of distance and displacement is crucial in analyzing the motion of objects, and this example illustrates how to calculate these quantities in a real-world scenario.

Discussion

What happens if the puck moves in a circular path? How would you calculate the distance and displacement in this case?
Can you think of a real-world scenario where the concepts of distance and displacement are important?
How would you calculate the displacement if the puck moves in a zigzag pattern?

Answers

If the puck moves in a circular path, you would calculate the distance as the circumference of the circle, and the displacement would be the radius of the circle.
A real-world scenario where the concepts of distance and displacement are important is in navigation, where pilots and sailors need to calculate their position and distance traveled to reach their destination.
If the puck moves in a zigzag pattern, you would calculate the displacement by finding the net distance traveled in a single direction, just like in the example above.

Additional Resources

For more information on distance and displacement, check out the following resources:

Khan Academy: Distance and Displacement
Physics Classroom: Distance and Displacement
MIT OpenCourseWare: Physics 8.01: Distance and Displacement

Final Thoughts

Calculating distance and displacement is a fundamental concept in physics, and it's essential to understand these quantities to analyze the motion of objects. By following the steps outlined in this article, you can calculate the total distance moved and the magnitude and direction of the displacement for any given motion.

Introduction

In our previous article, we explored the motion of a hockey puck that moves 28 meters southward, then 14 meters northward, and finally 4 meters southward. We calculated the total distance moved and determined the magnitude and direction of the displacement. In this article, we'll answer some frequently asked questions about the motion of the hockey puck.

Q&A

Q: What is the difference between distance and displacement?

A: Distance refers to the total length of the path traveled by an object, while displacement is a measure of the object's change in position. In other words, distance is a scalar quantity, while displacement is a vector quantity.

Q: How do you calculate the total distance moved?

A: To calculate the total distance moved, you need to add up the distances traveled in each direction. In the case of the hockey puck, the total distance moved is 28 meters southward + 14 meters northward - 4 meters southward = 34 meters.

Q: How do you calculate the magnitude and direction of the displacement?

A: To calculate the magnitude of the displacement, you need to find the net distance traveled in a single direction. In the case of the hockey puck, the net distance traveled southward is 28 meters - 14 meters = 14 meters. The direction of the displacement is southward, since the puck moves a net distance of 14 meters in that direction.

Q: What if the puck moves in a circular path?

A: If the puck moves in a circular path, you would calculate the distance as the circumference of the circle, and the displacement would be the radius of the circle.

Q: Can you think of a real-world scenario where the concepts of distance and displacement are important?

A: Yes, a real-world scenario where the concepts of distance and displacement are important is in navigation, where pilots and sailors need to calculate their position and distance traveled to reach their destination.

Q: How would you calculate the displacement if the puck moves in a zigzag pattern?

A: If the puck moves in a zigzag pattern, you would calculate the displacement by finding the net distance traveled in a single direction, just like in the example above.

Q: What is the difference between a scalar quantity and a vector quantity?

A: A scalar quantity is a quantity that has only magnitude, while a vector quantity is a quantity that has both magnitude and direction.

Q: Can you give an example of a scalar quantity?

A: Yes, an example of a scalar quantity is temperature. Temperature has only magnitude, and it does not have direction.

Q: Can you give an example of a vector quantity?

A: Yes, an example of a vector quantity is displacement. Displacement has both magnitude and direction.

Q: What is the unit of measurement for displacement?

A: The unit of measurement for displacement is typically meters (m).

Q: Can you think of a situation where the concept of displacement is important?

A: Yes, the concept of displacement is important in many situations, such as in navigation, physics, and engineering.

Conclusion

In conclusion, the motion of a hockey puck is a great example of how to calculate distance and displacement. By understanding the concepts of distance and displacement, you can analyze the motion of objects and make predictions about their future behavior.

Additional Resources

For more information on distance and displacement, check out the following resources:

Khan Academy: Distance and Displacement
Physics Classroom: Distance and Displacement
MIT OpenCourseWare: Physics 8.01: Distance and Displacement