Distance And Displacement Worksheet With Answer Key

Distance and Displacement Worksheet with Answer Key: A Comprehensive Guide

Understanding the difference between distance and displacement is crucial in physics, forming the foundation for more complex concepts like velocity and acceleration. This comprehensive worksheet will delve into the nuances of these two quantities, providing ample practice problems with detailed solutions. We'll explore various scenarios, focusing on both their similarities and critical distinctions. By the end, you'll have a solid grasp of distance and displacement, ready to tackle more advanced physics problems.

What is Distance?

Distance is a scalar quantity, meaning it only has magnitude (size). It represents the total length of the path traveled by an object. Regardless of the direction, the distance covered is added up. Think of it as the odometer in your car – it keeps track of the total distance driven, regardless of the route.

Key Characteristics of Distance:

• Scalar: Only magnitude, no direction.
• Always positive: Distance cannot be negative.
• Path-dependent: The specific route taken affects the total distance.

What is Displacement?

Displacement is a vector quantity, meaning it has both magnitude and direction. It represents the shortest distance between the starting point and the ending point of an object's motion. It's a straight line connecting the initial and final positions, irrespective of the actual path taken.

Key Characteristics of Displacement:

• Vector: Both magnitude and direction are crucial.
• Can be positive, negative, or zero: Directionality determines the sign.
• Path-independent: The actual path traveled does not affect displacement.

Distinguishing Distance and Displacement: Examples

Let's illustrate the difference with some examples:

Example 1: A car travels 5 km east, then 3 km north.

• Distance: The total distance traveled is 5 km + 3 km = 8 km.
• Displacement: The displacement is the straight-line distance from the starting point to the ending point. Using the Pythagorean theorem (a² + b² = c²), the displacement is √(5² + 3²) = √34 km, approximately 5.83 km. The direction would be specified as an angle relative to the east direction.

Example 2: A person walks 10 meters north, then 10 meters south.

• Distance: The total distance traveled is 10 m + 10 m = 20 m.
• Displacement: The displacement is 0 meters. The person ended up at the same point they started.

Example 3: A jogger runs around a circular track of 400 meters. After completing one lap, the jogger returns to the starting point.

• Distance: The distance covered is 400 meters.
• Displacement: The displacement is 0 meters, as the jogger finishes at the same point where they started.

Distance and Displacement Worksheet: Problems

Now let's practice with some problems. Remember to clearly indicate both distance and displacement for each scenario, including the direction for displacement.

Problem 1: A bird flies 10 m east, then 5 m south, and finally 2 m west. What is the total distance and displacement?

Problem 2: A car travels 20 km north, then 15 km south. Find the distance and displacement.

Problem 3: A hiker walks 3 km east, 4 km north, and then 2 km west. Calculate the total distance and displacement.

Problem 4: A ball rolls 5 meters along a straight line. What is the distance and displacement?

Problem 5: A cyclist rides 100 meters north, 50 meters east, 50 meters south and finally 100 meters west. Find the distance and displacement of the cyclist.

Problem 6: An athlete runs around a rectangular track with sides 100 meters and 50 meters. Calculate the total distance and displacement after he completes one lap.

Distance and Displacement Worksheet: Answer Key

Now, let's go through the solutions for the problems above:

Problem 1:

• Distance: 10 m + 5 m + 2 m = 17 m
• Displacement: Use vector addition. The net displacement in the east-west direction is 10 m - 2 m = 8 m east. The displacement in the north-south direction is 5 m south. The magnitude of the total displacement is √(8² + 5²) = √89 m ≈ 9.43 m. The direction is south of east (you can calculate the angle using trigonometry).

Problem 2:

• Distance: 20 km + 15 km = 35 km
• Displacement: 20 km - 15 km = 5 km north.

Problem 3:

• Distance: 3 km + 4 km + 2 km = 9 km
• Displacement: The net displacement in the east-west direction is 3 km - 2 km = 1 km east. The displacement in the north-south direction is 4 km north. The magnitude of the total displacement is √(1² + 4²) = √17 km ≈ 4.12 km. The direction is north of east (you can calculate the angle using trigonometry).

Problem 4:

• Distance: 5 meters
• Displacement: 5 meters in the direction of motion.

Problem 5:

• Distance: 100 m + 50 m + 50 m + 100 m = 300 m
• Displacement: The net displacement in the north-south direction is 100 m - 50 m = 50 m north. The net displacement in the east-west direction is 50 m east - 100 m west = -50 m (or 50m west). The magnitude of the total displacement is √(50² + 50²) = √5000 m ≈ 70.7 m. The direction is northwest (45 degrees).

Problem 6:

• Distance: The perimeter of the rectangle is 2 * (100 m + 50 m) = 300 m.
• Displacement: 0 m. The athlete returns to the starting point.

Advanced Concepts and Applications

Understanding distance and displacement is fundamental to grasping more advanced physics concepts. These include:

• Velocity and Speed: Velocity is the rate of change of displacement, while speed is the rate of change of distance. Velocity is a vector, and speed is a scalar.
• Acceleration: Acceleration is the rate of change of velocity. It's a vector quantity.
• Projectile Motion: Analyzing the trajectory of a projectile involves understanding both distance and displacement components.
• Relative Motion: Determining the motion of an object relative to another requires careful consideration of both distance and displacement.

This worksheet provides a foundational understanding, paving the way for more complex calculations and applications in kinematics and other areas of physics. Remember to always clearly define your coordinate system and carefully consider both magnitude and direction when dealing with vector quantities. Consistent practice is key to mastering these concepts.