Chapter 2: Problem 4
Identify Does an odometer in a car measure distance or displacement? Explain.
Short Answer
Expert verified
An odometer measures distance, not displacement.
Step by step solution
01
Understand the Terms
First, we need to understand the terms 'distance' and 'displacement'. Distance refers to the total path length traveled by an object, irrespective of its start or end point direction. Displacement, on the other hand, is a vector quantity that refers to the change in position of an object from its starting point to its ending point.
02
Identify the Odometer's Function
An odometer is an instrument used in vehicles that measures how much ground the vehicle has covered. It tracks the entire path by counting the number of revolutions made by the wheels.
03
Compare Distance and Displacement Measurement
Since an odometer measures how many miles or kilometers a vehicle has traveled, it records the total path taken. Regardless of the direction or if the car returns to the starting point, the odometer continues to increase, similar to distance.
04
Conclude the Measurement
Considering the definitions and the functioning of an odometer, it is clear that an odometer measures distance, not displacement, because it adds up the entire path traveled without concern for direction or final position change.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Distance vs Displacement
The concepts of distance and displacement are often confused, yet they are quite different. Both involve movement but measure it in distinct ways.
- Distance: This is the total path length that an object travels, regardless of its starting or ending position. Imagine driving around city blocks. Even if you end up back where you started, your odometer won't reflect "zero" because it measures all the paths you've taken, not your position relative to the start.
- Displacement: This is a vector quantity, meaning it has both magnitude and direction. It reflects the change in position from your starting point to your end point. If you drove around a block and returned to your starting place, your displacement would be zero because there's no change in your initial position.
Vector Quantity
In physics, some quantities, like displacement, speed, and force, are vectors. Vectors have both magnitude and direction, which makes them crucial for describing physical phenomena involving direction.
A vector can be represented by an arrow; the length represents magnitude and the arrowhead, direction. For instance, displacement involves a straight line from the start to the end point, with directionality being a crucial factor.
Always remember:
- A vector answers both "how much?" and "which way?"
- Vectors are used to describe forces, as the direction of a force is as vital as its strength.
- Examples of vector quantities include velocity, acceleration, and displacement.
Vehicle Instrumentation
Vehicles are equipped with various instruments, each designed to keep tabs on different aspects of your journey. One of the key instruments is the odometer.
An odometer tracks how far a vehicle's wheels have rolled, essentially counting the total revolutions. With this data, it calculates the distance traveled.
Here's how it differs from other instruments:
- Odometer: Measures distance traveled; it doesn't consider direction. Driven entirely by wheel rotation, providing a simple yet effective way to gauge how much ground you've covered.
- Compass or GPS: Unlike the odometer, these instruments factor in direction and can pinpoint locations, providing displacement measurements.
- Speedometer: Shows current speed without directionality, indicating how fast you're traveling at any given moment.