/*! 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 19 A cyclist is travelling on a cir... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 19

A cyclist is travelling on a circular section of highway of radius \(2500 \mathrm{ft}\) at the speed of 60 mile/h. The cyclist suddenly applies the brakes causing the bicycle to slow down at constant rate. Knowing that after eight second, the speed has been reduced to 45 mile/h. The acceleration of the bicycle immediately after the brakes have been applied is: (a) \(2 \mathrm{ft} / \mathrm{s}^{2}\) (b) \(4.14 \mathrm{ft} / \mathrm{s}^{2}\) (c) \(3.10 \mathrm{ft} / \mathrm{s}^{2}\) (d) \(2.75 \mathrm{ft}^{2} / \mathrm{s}\)

Short Answer

Expert verified
The acceleration is 2.75 ft/s虏, matching option (d).

Step by step solution

01

Understanding the Given Values

We know that the initial velocity of the cyclist is 60 miles per hour, and after 8 seconds, it reduces to 45 miles per hour. First, we need to convert these velocities from miles per hour to feet per second because it is required for our calculation. Let's convert the speeds.
02

Convert Velocities to ft/s

The initial velocity, \( v_i = 60 \) miles/hour. Convert to feet per second: \( 60 \times \frac{5280}{3600} = 88 \text{ ft/s} \). The final velocity, \( v_f = 45 \) miles/hour. Convert to feet per second: \( 45 \times \frac{5280}{3600} = 66 \text{ ft/s} \).
03

Calculate Deceleration

Using the formula for constant acceleration, \( a = \frac{v_f - v_i}{t} \), where \( t = 8 \) seconds, \( v_i = 88 \) ft/s, and \( v_f = 66 \) ft/s, we can find the deceleration (negative acceleration) of the bicycle.
04

Solve for Acceleration

Substitute the values into the equation: \( a = \frac{66 - 88}{8} = \frac{-22}{8} = -2.75 \text{ ft/s}^2 \). Note that the negative sign indicates deceleration.
05

Decide on the Correct Option

The absolute value of the calculated acceleration is \( 2.75 \text{ ft/s}^2 \). Looking at the options provided in the question, the correct answer is option (d), \( 2.75 \text{ ft}^2/\text{s} \).

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.

Acceleration
Acceleration is a fundamental concept in physics. It's defined as the rate at which an object changes its velocity. This means that if an object speeds up, slows down, or changes direction, it is experiencing acceleration. The formula to calculate acceleration is \( a = \frac{v_f - v_i}{t} \), where \( v_f \) is the final velocity, \( v_i \) is the initial velocity, and \( t \) is the time over which the change occurs. This measures how quickly something speeds up or down over time.
  • An increase in velocity leads to positive acceleration.
  • A decrease in velocity leads to negative acceleration, also known as deceleration.
Understanding acceleration is crucial in various fields, from designing transportation systems to understanding natural phenomena.
Deceleration
Deceleration is a specific type of acceleration when the velocity of an object decreases. In other words, it refers to the negative acceleration that occurs when an object slows down. In the given exercise, the cyclist applies brakes to reduce speed鈥攖his is a classic example of deceleration.
To calculate deceleration, use the same formula as acceleration: \( a = \frac{v_f - v_i}{t} \). Here, the initial velocity \( v_i \) is larger than the final velocity \( v_f \), resulting in a negative value for \( a \), i.e., \( a = \frac{66 - 88}{8} = -2.75 \text{ ft/s}^2 \).
  • Deceleration is indicated by a negative sign in calculations.
  • It's a crucial factor for safety in transport systems, like bicycles or cars, when calculating stopping distances and required braking forces.
Conversion of Units
Understanding how to convert units is essential in physics, especially when dealing with velocity and acceleration. In the original exercise, the cyclist's speed is initially given in miles per hour (mph), but the calculations need to be made in feet per second (ft/s). This is a common requirement when solving problems related to dynamics.
To convert from miles per hour to feet per second:
  • 1 mile per hour is approximately equal to 1.467 feet per second.
  • Multiply the speed in miles per hour by \( \frac{5280}{3600} \) (since there are 5280 feet in a mile and 3600 seconds in an hour) to get the speed in feet per second.
For example, converting 60 mph to ft/s:
  • 60 mph = 60 \times \frac{5280}{3600} = 88 \text{ ft/s}.
Accurate unit conversion ensures all parts of the problem are aligned correctly to get a precise solution. It's essential for engineering, physics, and any science involving practical calculations.

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 cyclist goes round a circular path of length \(400 \mathrm{~m}\) in 20 second. The angle through which he bends from vertical in order to maintain the balance is: (a) \(\sin ^{-1}(0.64)\) (b) \(\tan ^{-1}(0.64)\) (c) \(\cos ^{-1}(0.64)\) (d) none of these

A boat which is rowed with constant velocity \(u\), starts from point \(A\) on the bank of river which flows with a constant velocity \(v\) and it points always towards a point B. On the other bank exactly opposite to \(A\), the equation of the path of boat is: (a) \(r \sin \theta=c\left(\tan \frac{\theta}{2}\right)^{1 / v}\) (b) \(r \sin \theta=\frac{u}{v}\) (c) \(r^{2} \sin \theta=\frac{u}{v}\) (d) \(u r^{2}=v \sin ^{2} \theta\) (e) none of the above

The skate board negotiates the circular surface of radius \(4.5 \mathrm{~m}\) (shown in the figure). At \(\theta=45^{\circ}\), its speed of centre of mass is \(6 \mathrm{~m} / \mathrm{s}\). The combined mass of skate board and the person is \(70 \mathrm{~kg}\) and his centre of mass is \(0.75 \mathrm{~m}\) from the surface. The normal reaction between the surface and the skate board wheel is: (a) \(500 \mathrm{~N}\) (b) \(2040 \mathrm{~N}\) (c) \(1045 \mathrm{~N}\) (d) zero

A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle \(\phi\) as \(\omega=\omega_{0}-k \phi\) where \(\omega_{0}\) and \(k\) are positive constants. At the moment \(t=0, \phi=0\), the time dependence of rotation angle is: (a) \(k \omega_{0} e^{-k t}\) (b) \(\frac{\omega_{0}}{k} e^{-k t}\) (c) \(\frac{\omega_{0}}{k}\left(1-e^{-k t}\right)\) (d) \(\frac{k}{\omega_{0}}\left(e^{-k t}-1\right)\)

Particles are released from rest at \(A\) and slide down the smooth surface of height \(h\) to a conveyor \(B\). The correct angular velocity \(\omega\) of the conveyor pulley of radius \(r\) to prevent any sliding on the belt as the particles transfer to the conveyor is: (a) \(\sqrt{2 g h}\) (b) \(\frac{2 g h}{r}\) (c) \(\frac{\sqrt{2 g h}}{r}\) (d) \(\frac{2 g h^{2}}{r^{2}}\)
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Modern Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Physics of Motion

Read Explanation

Classical Mechanics

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.