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Consider a coordinate system in which the positive \(x\) axis is directed upward vertically. What are the positions of a particle (a) \(5.0 \mathrm{m}\) directly above the origin and (b) \(2.0 \mathrm{m}\) below the origin?

Short Answer

Expert verified
The position of the particle directly above the origin is at \(x=5.0 m\) and the particle below the origin is at \(x=-2.0 m\).

Step by step solution

01

Identify the positions

In a coordinate system where the positive x-axis is directed upward, any point above the origin is a positive distance, while any point below the origin is a negative distance from the origin.
02

Position of the particle directly above the origin

The particle is \(5.0 m\) directly above the origin, which means it is \(5.0 m\) along the positive x-axis. Thus, the position of the particle is \(x=5.0 m\).
03

Position of the particle below the origin

The particle that is \(2.0 m\) below the origin, is \(2.0 m\) along the negative x-axis. Thus, the position of the particle is \(x=-2.0 m\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Particle Position
In physics, understanding the concept of particle position is fundamental for studying motion. Imagine you have a map, and you want to pinpoint a specific location; in physics, you use a coordinate system to do exactly that for particles. Position is noted as a distance from a reference point, commonly called the origin. In the example provided, the origin is seen as ground level.

In the given exercise scenario, with the positive x-axis pointing upwards, the position of a particle placed above the origin is expressed with a positive number. This reflects the conventional direction we assign to the axis. So, if a particle is 5.0 meters above the origin, we describe its position as being at +5.0 meters. This positive numerical value is not just a distance, but it also gives us directional information, telling us the particle is above the reference point.
Positive and Negative Directions

Interpreting Directions in Physics

When studying motion, it's important to distinguish not just how far something is from a reference point, but also in which direction. Positive and negative signs serve this purpose in one-dimensional motion. Positive typically signifies one direction (upward, rightward, or forward), while negative indicates the opposite (downward, leftward, or backward).

In the scenario from the exercise, a particle below the starting point, which is 2.0 meters downward, is marked with a negative sign, indicating that it is in the opposite direction to the positive x-axis. The choice of positive and negative directions can be arbitrary, but once established, it allows us to communicate and calculate motion consistently.
One-dimensional Motion

Simplifying Complex Motions

In physics, one-dimensional motion refers to movement in a straight line. This simplification allows us to discuss and analyze motion without the complications of turns or curves. For students beginning to learn about kinematics, which is the study of motion without considering its causes, one-dimensional analyses provide a solid foundation.

Whether an object is moving upward, downward, left, right, forward, or backward, as long as it's in a straight line, we can use one-dimensional motion concepts. The everyday implications of this include things like an elevator going up or down a shaft, a sprinter running a 100-meter dash, or even a rock being dropped into a well. Each of these can be evaluated using the principles of one-dimensional motion by assigning positive and negative directions and calculating positions and velocities accordingly.

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Most popular questions from this chapter

Suppose you throw a rock nearly straight up at a coconut in a palm tree and the rock just misses the coconut on the way up but hits the coconut on the way down. Neglecting air resistance and the slight horizontal variation in motion to account for the hit and miss of the coconut, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the coconut on the way up? Is it more likely to dislodge the coconut on the way up or down? Explain.

(a) A light-rail commuter train accelerates at a rate of \(1.35 \mathrm{m} / \mathrm{s}^{2} .\) How long does it take to reach its top speed of 80.0 \(\mathrm{km} / \mathrm{h}\), starting from rest? (b) The same train ordinarily decelerates at a rate of \(1.65 \mathrm{m} / \mathrm{s}^{2} .\) How long does it take to come to a stop from its top speed? (c) In emergencies, the train can decelerate more rapidly, coming to rest from \(80.0 \mathrm{km} / \mathrm{h}\) in \(8.30 \mathrm{s}\). What is its emergency acceleration in meters per second squared?

Professional baseball player Nolan Ryan could pitch a baseball at approximately \(160.0 \mathrm{km} / \mathrm{h}\). At that average velocity, how long did it take a ball thrown by Ryan to reach home plate, which is \(18.4 \mathrm{m}\) from the pitcher's mound? Compare this with the average reaction time of a human to a visual stimulus, which is \(0.25 \mathrm{s}\).

A raindrop falls from a cloud \(100 \mathrm{m}\) above the ground. Neglect air resistance. What is the speed of the raindrop when it hits the ground? Is this a reasonable number?

In a 100 -m race, the winner is timed at 11.2 s. The second-place finisher's time is 11.6 s. How far is the second-place finisher behind the winner when she crosses the finish line? Assume the velocity of each runner is constant throughout the race.

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