Distance And Displacement Worksheet With Answers: Easy Guide
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Distance and displacement are fundamental concepts in physics that help us understand motion. Whether you are a student learning about these terms for the first time or someone looking to brush up on your knowledge, this guide provides a comprehensive overview along with a worksheet and answers to reinforce your understanding. 📚
Understanding Distance and Displacement
What is Distance? 📏
Distance refers to the total path length traveled by an object, regardless of the direction. It is a scalar quantity, meaning it only has magnitude and no direction. For instance, if you walk 3 kilometers to the store and then 2 kilometers back, the total distance you covered is:
[ \text{Distance} = 3 , \text{km} + 2 , \text{km} = 5 , \text{km} ]
What is Displacement? ↔️
Displacement, on the other hand, is a vector quantity that refers to the shortest straight-line distance from the starting point to the endpoint in a specific direction. It takes into account both the magnitude and direction. Using the previous example, your displacement would be:
[ \text{Displacement} = 2 , \text{km} - 3 , \text{km} = -1 , \text{km} ]
This means you are 1 kilometer away from your starting point in the opposite direction of your walk to the store.
Key Differences
To summarize the differences between distance and displacement, take a look at the table below:
<table> <tr> <th>Feature</th> <th>Distance</th> <th>Displacement</th> </tr> <tr> <td>Type</td> <td>Scalar</td> <td>Vector</td> </tr> <tr> <td>Path</td> <td>Path taken</td> <td>Straight line</td> </tr> <tr> <td>Direction</td> <td>No direction</td> <td>Has direction</td> </tr> <tr> <td>Example</td> <td>5 km</td> <td>1 km (to the west)</td> </tr> </table>
Why Are They Important?
Understanding distance and displacement is crucial in various fields, including physics, engineering, and everyday life. They play a significant role in calculating speed, velocity, and acceleration, which are fundamental concepts in motion.
Distance and Displacement Worksheet
Now that you have a grasp of the basic concepts, let’s put that knowledge to the test! Here is a worksheet designed to help you practice calculating distance and displacement.
Worksheet Questions
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A car travels 10 km east, then 5 km north. What is the total distance traveled by the car? What is its displacement?
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A runner goes around a track and completes one lap of 400 meters. What is the distance covered and what is the displacement?
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A person walks 4 km west, then turns around and walks 1 km east. What is their total distance and displacement?
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A cyclist moves 12 km south, then 9 km east. Calculate both the distance and the displacement.
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A bird flies 8 km in a straight line from point A to point B and then 6 km back to point A. What is the total distance flown, and what is the bird's displacement from point A?
Important Note
Always remember to define the direction when calculating displacement! Directions such as north, south, east, and west can greatly affect your answer. 🧭
Worksheet Answers
Here are the solutions to the worksheet questions:
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Distance: 10 km + 5 km = 15 km
Displacement: Use Pythagorean theorem:
[ \sqrt{(10^2 + 5^2)} = \sqrt{100 + 25} = \sqrt{125} \approx 11.18 , \text{km} , \text{north-east} ] -
Distance: 400 meters
Displacement: 0 meters (because the starting and ending points are the same) -
Distance: 4 km + 1 km = 5 km
Displacement: 4 km west - 1 km east = 3 km west -
Distance: 12 km + 9 km = 21 km
Displacement: Use Pythagorean theorem:
[ \sqrt{(12^2 + 9^2)} = \sqrt{144 + 81} = \sqrt{225} = 15 , \text{km} , \text{south-east} ] -
Distance: 8 km + 6 km = 14 km
Displacement: 0 km (since the bird ends up back at point A)
Conclusion
Understanding the concepts of distance and displacement is essential for anyone studying motion. By practicing with the provided worksheet, you can solidify your understanding and improve your problem-solving skills in physics. Remember to take your time and carefully analyze each problem, as the distinction between distance and displacement is crucial for accurate calculations. 🚀 Happy learning!