/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 72 You may have noticed while drivi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 72

You may have noticed while driving that your car's velocity does not continue to increase, even though you keep your foot on the gas pedal. This behavior is due to air resistance and friction between the moving parts of the car. Figure 2.48 shows a qualitative \(v_{x^{-}} t\) graph for a typical car if it starts from rest at the origin and travels in a straight line (the \(x\) -axis). Sketch qualitative \(a_{x}-t\) and \(x-t\) graphs for this car.

Short Answer

Expert verified
The car's acceleration decreases to zero, while the position increases linearly over time.

Step by step solution

01

Understand the Graph Types

The question asks for two separate sketches: an acceleration-time \((a_x-t)\) graph and a position-time \((x-t)\) graph based on an already provided velocity-time \((v_x-t)\) graph. It's noted that our car starts from rest and travels on a straight line.
02

Analyze the Velocity-Time Graph

Since we don't have the actual graph, we consider a typical behavior where velocity starts at zero because the car starts from rest, increases quickly initially, and then levels off due to factors like air resistance and friction.
03

Sketch the Acceleration-Time Graph

The \((a_x-t)\) graph should reflect initially high acceleration as the car speeds up, reducing over time as the car reaches a constant velocity (due to air resistance). This results in a graph that starts high and decreases to zero.
04

Sketch the Position-Time Graph

The \((x-t)\) graph will show the car starting at zero. Initially, the position increases slowly, then at a steady increasing rate when acceleration is strong, and finally, approaches a linear growth as velocity becomes constant.

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 91影视!

Key Concepts

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

Velocity-Time Graph
A velocity-time graph, or \(v_x-t\) graph, is an indispensable tool in kinematics. It portrays how velocity changes over time. In our scenario, the car begins at rest, so its initial velocity is zero. As the driver presses the gas pedal, the car's velocity increases, indicating a rising line on the graph.

However, the car's velocity doesn't increase indefinitely. Due to forces like air resistance and friction, the velocity levels off. This means the graph transitions into a horizontal line, showing that the car has reached a constant velocity.

Understanding this graph is crucial as it forms the foundation for other related graphs. Let's delve deeper into how these changes in velocity affect acceleration and position over time.
Acceleration-Time Graph
The acceleration-time graph, or \(a_x-t\) graph, showcases how acceleration varies as time passes. When a car first starts moving from rest, it typically experiences high acceleration. This period is when the driver feels the initial push as the car speeds up. The graph reflects this with a high point at the beginning.

As time goes on, this acceleration begins to decrease because of factors such as air resistance. This slowing of acceleration is depicted as a descending line on the graph. Eventually, as the car reaches a constant velocity, acceleration reduces to zero, resulting in the graph flattening out at zero.

Grasping the \(a_x-t\) graph is fundamental in predicting the car's behavior through its changes in acceleration, and it seamlessly links to how the car's position is altered over time.
Position-Time Graph
A position-time graph, or \(x-t\) graph, helps visualize how the position of an object, like a car, changes over a period. Initially, as the car's velocity and acceleration pick up, the position changes slowly but begins to curve upward鈥攊ndicating increasing speed.

As acceleration reaches its peak and starts to decline, you can see a more linear pattern emerging on the graph. This linear growth occurs when the car maintains a constant velocity without further acceleration.

The beauty of the \(x-t\) graph lies in its ability to depict not just the car's travel over time, but also hint at different phases of motion derived from its acceleration and velocity changes. Through understanding this graph, one can draw meaningful connections between position, velocity, and acceleration.

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

During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.30 \(\mathrm{m} / \mathrm{s}^{2} .\) When it is 235 \(\mathrm{m}\) above the launch pad, it discards a used fuel canister by simply disconnecting it. Once it is disconnected, the only force acting on the canister is gravity (air resistance can be ignored). (a) How high is the rocket when the canister hits the launch pad, assuming that the rocket does not change its acceleration? (b) What total distance did the canister travel between its release and its crash onto the launch pad?

A subway train starts from rest at a station and accelerates at a rate of 1.60 \(\mathrm{m} / \mathrm{s}^{2}\) for 14.0 \(\mathrm{s}\) . It runs at constant speed for 70.0 \(\mathrm{s}\) and slows down at a rate of 3.50 \(\mathrm{m} / \mathrm{s}^{2}\) until it stops at the next station. Find the total distance covered.

You are standing at rest at a bus stop. A bus moving at a constant speed of 5.00 m/s passes you. When the rear of the bus is 12.0 m past you, you realize that it is your bus, so you start to run toward it with a constant acceleration of 0.960 m/s. How far would you have to run before you catch up with the rear of the bus, and how fast must you be running then? Would an average college student be physically able to accomplish this?

Sam heaves a \(16-\) - Ib shot straight upward, giving it a constant upward accleration from rest of 45.0 \(\mathrm{m} / \mathrm{s}^{2}\) for 64.0 \(\mathrm{cm} .\) He releases it 2.20 \(\mathrm{m}\) above the ground. You may ignore air resistance. \((\mathrm{a})\) What is the speed of the shot when Sam releases it? (b) How high above the ground does it go? (c) How much time does he have to get out of its way before it returns to the height of the top of his head, 1.83 \(\mathrm{m}\) above the ground?

Dan gets on Interstate Highway \(\mathrm{I}-80\) at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88 \(\mathrm{km} / \mathrm{h}\) . After traveling 76 \(\mathrm{km}\) , he reaches the Aurora exit (Fig. 2.44\()\) . Realizing he has gone too far, he turns around and drives due east 34 \(\mathrm{km}\) back to the York exit at an average velocity of magnitude 72 \(\mathrm{km} / \mathrm{h}\) . For his whole trip from Seward to the York exit, what are (a) his average speed and (b) the magnitude of his average velocity?
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Electricity and Magnetism

Read Explanation

Magnetism

Read Explanation

Atoms and Radioactivity

Read Explanation

Mechanics and Materials

Read Explanation

Kinematics Physics

Read Explanation
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.