Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 34

An airplane lands and starts down the runway with a southwest velocity of $55 \mathrm{m} / \mathrm{s}$. What constant acceleration allows it to come to a stop in \(1.0 \mathrm{km} ?\)

Short Answer

Expert verified
Answer: The constant acceleration required for the airplane to come to a stop in 1.0 km is -1.51 m/s².

Step by step solution

01

List the known quantities

We know the following: - Initial Velocity \((v_i)\): \(55~m/s\) (southwest) - Final Velocity \((v_f)\): \(0~m/s\) (since the airplane comes to a stop) - Displacement \((d)\): \(1000~m\) (1.0 km)
02

Choose the appropriate equation of motion

We can choose the equation of motion that relates initial velocity, final velocity, acceleration, and displacement: \(v_f^2 = v_i^2 + 2ad\)
03

Solve for acceleration

Using the equation of motion from Step 2, we can plug in the known values and solve for the acceleration (\(a\)): \((0~m/s)^2 = (55~m/s)^2 + 2ad\) \(0 = 55^2 + 2ad\) Now, we'll isolate \(a\) on one side of the equation: \(-55^2 = 2ad\) Now divide both sides by \(2d\): \( a = \frac{-55^2}{2(1000)}\)
04

Calculate the acceleration

Calculate the acceleration (\(a\)) using the numbers in the equation: \( a = \frac{-55^2}{2(1000)}\) \( a = \frac{-3025}{2000} \approx -1.51~m/s^2\) The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which is the case because the airplane is decelerating to come to a stop. Thus, the constant acceleration required for the airplane to come to a stop in 1.0 km is \(-1.51~m/s^2\).

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.

Start your free trial

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

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

please assume the free-fall acceleration \(g=9.80 \mathrm{m} / \mathrm{s}^{2}\) unless a more precise value is given in the problem statement. Ignore air resistance. A penny is dropped from the observation deck of the Empire State building (369 m above ground). With what velocity does it strike the ground?
In the problems, please assume the free-fall acceleration $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ unless a more precise value is given in the problem statement. Ignore air resistance. 56\. (a) If a freestyle swimmer traveled \(1500 \mathrm{m}\) in a time of $14 \mathrm{min} 53 \mathrm{s},$ how fast was his average speed? (b) If the pool was rectangular and \(50 \mathrm{m}\) in length, how does the speed you found compare with his sustained swimming speed of \(1.54 \mathrm{m} / \mathrm{s}\) during one length of the pool after he had been swimming for 10 min? What might account for the difference?
You are driving your car along a country road at a speed of $27.0 \mathrm{m} / \mathrm{s} .$ As you come over the crest of a hill, you notice a farm tractor \(25.0 \mathrm{m}\) ahead of you on the road, moving in the same direction as you at a speed of \(10.0 \mathrm{m} / \mathrm{s} .\) You immediately slam on your brakes and slow down with a constant acceleration of magnitude $7.00 \mathrm{m} / \mathrm{s}^{2} .$ Will you hit the tractor before you stop? How far will you travel before you stop or collide with the tractor? If you stop, how far is the tractor in front of you when you finally stop?
In the problems, please assume the free-fall acceleration $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ unless a more precise value is given in the problem statement. Ignore air resistance. To pass a physical fitness test, Marcella must run \(1000 \mathrm{m}\) at an average speed of \(4.00 \mathrm{m} / \mathrm{s} .\) She runs the first $500 \mathrm{m}\( at an average of \)4.20 \mathrm{m} / \mathrm{s} .$ (a) How much time does she have to run the last \(500 \mathrm{m} ?\) (b) What should be her average speed over the last \(500 \mathrm{m}\) in order to finish with an overall average speed of \(4.00 \mathrm{m} / \mathrm{s} ?\)
In a cathode ray tube in an old TV, electrons are accelerated from rest with a constant acceleration of magnitude $7.03 \times 10^{13} \mathrm{m} / \mathrm{s}^{2}\( during the first \)2.0 \mathrm{cm}$ of the tube's length; then they move at essentially constant velocity another \(45 \mathrm{cm}\) before hitting the screen. (a) Find the speed of the electrons when they hit the screen. (b) How long does it take them to travel the length of the tube?
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Radiation

Read Explanation

Wave Optics

Read Explanation

Quantum Physics

Read Explanation

Dynamics

Read Explanation

Torque and Rotational Motion

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.

Sign-up for free