Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

The initial position of an object that moves with constant velocity is increased. Does this change the intercept or the slope of the position-time graph of the object's motion? Explain.

Short Answer

Expert verified
Changing initial position affects the intercept, not the slope.

Step by step solution

01

Understand the Position-Time Graph

A position-time graph depicts the position of an object (usually on the y-axis) as it varies with time (on the x-axis). If an object is moving with constant velocity, this graph is represented by a straight line.
02

Intercept and Slope Concept

In the context of the position-time graph, the *intercept* is the point where the line crosses the y-axis, which represents the position of the object at time zero. The *slope* of the line represents the velocity of the object.
03

Impact of Changing Initial Position

Increasing the initial position means you are changing the y-intercept because the object starts at a higher position on the y-axis at time zero. The slope, representing the velocity, remains unchanged since velocity is constant.
04

Conclusion

Increasing the initial position changes the y-intercept of the position-time graph while the slope remains constant, indicating that velocity is unchanged.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

Constant Velocity
When an object moves at a constant velocity, its speed and direction stay the same over time. This means the object covers equal distances in equal intervals of time. In the context of a position-time graph, constant velocity is depicted as a straight line because the position of the object changes uniformly with time.
  • A steeper slope indicates a higher velocity.
  • A flatter slope shows a slower velocity.
A straight-line graph means there's no acceleration involved, just steady speed.
Y-Intercept
The y-intercept on a position-time graph represents the initial position of the object at the starting point, which is typically time zero. It is the point where the line crosses the y-axis.
  • Changing the initial position of the object will result in a change in the y-intercept.
  • The intercept value provides a clear snapshot of where the object begins its motion.
Increase the initial position, and you'll see the y-intercept shift upward. Lower it, and the intercept will move down.
Slope
The slope of a position-time graph is crucial because it represents the velocity of the object. A slope is essentially a measure of how steep the line is, which translates to how quickly the position is changing over time.
  • Calculated as \( \text{slope} = \frac{\Delta y}{\Delta x} \) where \( \Delta y \) is the change in position, and \( \Delta x \) is the change in time.
  • A positive slope means the object is moving forward.
  • A negative slope indicates backward movement.
With a constant velocity, the slope remains unchanged even if the initial position is altered.
Initial Position
The initial position is where the object starts its journey in a position-time graph. This position determines the y-intercept of the graph but does not affect the slope.
  • If you increase the initial position, it shifts the line up on the graph without changing its angle.
  • If you decrease it, the line shifts lower.
  • This parameter shows where exactly the object was at the beginning of observation.
The initial position establishes the starting point of the line, ensuring that changes don't impact velocity, hence the slope remains constant.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A soccer ball rests on the field at the location \(x=5.0 \mathrm{~m}\). Two players run along the same straight line toward the ball. Their equations of motion are as follows: $$ \begin{aligned} &x_{1}=-8.2 \mathrm{~m}+(4.2 \mathrm{~m} / \mathrm{s}) t \\ &x_{2}=-7.3 \mathrm{~m}+(3.9 \mathrm{~m} / \mathrm{s}) t \end{aligned} $$ (a) Which player is closer to the ball at \(t=0\) ? (b) At what time does one player pass the other player? (c) What is the location of the players when one passes the other?

Make a position-time graph for a particle that is at \(x=3.1 \mathrm{~m}\) at \(t=0\) and moves with a constant velocity of \(-2.7 \mathrm{~m} / \mathrm{s}\). Plot the motion for the range \(t=0\) to \(t=6.0 \mathrm{~s}\).

Make a position-time graph for a particle that is at \(x=5.0 \mathrm{~m}\) at \(t=0\) and moves with a constant velocity of \(3.5 \mathrm{~m} / \mathrm{s}\). Plot the motion for the range \(t=0\) to \(t=6.0 \mathrm{~s}\).

Two dragonflies have the following equations of motion: $$ \begin{aligned} &x_{1}=2.2 \mathrm{~m}+(0.75 \mathrm{~m} / \mathrm{s}) t \\ &x_{2}=-3.1 \mathrm{~m}+(-1.1 \mathrm{~m} / \mathrm{s}) t \end{aligned} $$ (a) Which dragonfly is moving faster? (b) Which dragonfly starts out closer to \(x=0\) at \(t=0\) ?

You travel from the location \(x_{\mathrm{i}}=20 \mathrm{~m}\) to the location \(x_{\mathrm{f}}=25 \mathrm{~m}\). Your friend travels from \(x_{\mathrm{i}}=35 \mathrm{~m}\) to \(x_{\mathrm{f}}=30 \mathrm{~m}\). Which of you has a positive displacement? Which of you has a negative displacement? Explain.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free