Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Freeway ramps. In designing a freeway on-ramp, you must make it long enough for cars to be able to accelerate and merge safely with traffic traveling at speeds of 70 mph. For an off-ramp, the cars must be able to come to a stop from 70 mph over the length of the ramp. Your traffic engineers provide the following data: Powerful cars can accelerate from rest to 60 mph in 5.0 s, while less powerful cars take twice as long to do this. When slowing down from 60 mph, a car with good tire treads will take 12.0 s to stop, whereas one with bald tires takes 20.0 s. In order to safely accommodate all the types of vehicles, what should be the minimum length (in meters) of on-ramps and off-ramps? Assume constant acceleration.

$=1072 \mathrm{m}$

Physics 101 Mechanics

Chapter 2

Motion along a Straight Line

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

University of Sheffield

McMaster University

Lectures

03:28

Newton's Laws of Moti…

04:16

In mathematics, a proof is…

04:15

Freeway Traffic. According…

04:31

Entering the freeway. A ca…

02:10

Entering the Freeway. A ca…

04:07

A car sits on an entrance …

06:56

Engineering a highway curv…

03:56

Highway Design To allow en…

06:49

As a highway engineer, you…

10:25

When highway curves are de…

03:26

Maximum Safe Speed. As you…

03:08

A traffic engineer monitor…

04:50

Speed Limits Studies by th…

04:03

CE Predict/Explain On two …

06:54

Along a straight road thro…

01:38

New studies by Federal Hig…

05:57

Constructing a Highway A h…

05:11

What's the fastest wa…

01:50

00:46

Automobile traffic passes …

06:03

In a stunt being filmed fo…

05:00

A car is behind a truck go…

so we essentially to figure out the minimum length for the on ramp and then the minimum length for the off ramp. So we know that the V of X final equals 60 miles per hour, and the the time it takes for a slow car to accelerate to 60 miles per hour is going to be two times the time it takes for a fast car. Take salary to 60 miles per hour, so this will be equal to 10 seconds. Using this information, we have to make the ramp first fast and slow cars. So we need to make the acceleration for slow cars because fast cars can always accomodate. But slow cars, of course, can't move faster than their maximum acceleration. Sweet can save the X Final equals V X initial plus a T slow. You know the X final equals zero because they're trying to merge onto the highway. So we have the acceleration will be equal to 60 miles per hour, and then we're going to convert 10 years per second. So 16 09 meters per mile and then for every one hour there are 36 100 seconds and this will be divided by 10 seconds The total time and this equals 2.862 meters per second squared now to find that the length of the on ramp, we need to say that v x final squared equals v X Initial squared plus two ace of x times Delta X Now here we need Delta X So we're going to solve For Delta X, this equals v X final squared, divided by to sew a two times a sub x again the final rather the initial squared here is going to be zero. However, VI final squared here is going to be 70 miles per hour because again, this is only the first step was only to find the acceleration. The second step is used to find the distance and again in order to merge onto the highway. You need it, you need it. Ah, at least a speed of 70 miles per hour. So this acceleration does apply. But the VX final now is going to be 70 miles per hour. So we have 70 times 1,609 times one divided by 3 36 100 This is going to be squared and then this will be divided by two times the acceleration. So two times 2.862 and we have Delta X equaling 171 meters. So this would be the minimum distance for on grams and this would be our final answer for the first part. And for the second part, we know that the ex initial equals 60 miles per hour. We're trying to find the length of the off ramp now, and we know that it takes slow cars 20 seconds to decelerate from 60 miles per hour to rest. So we can say that the X final equals of the ex initial plus a team you know, the VX final equal zero. So a is going to be able to negative the ex initial divided by t. This will be equal Teo six again 60 times 16 09 times one divided by 36 100. And this will be divided rather negative. And this will be divided by T 20 seconds. And this is giving us negative 1.3 for one meters per second squared. So this would be the accept the maximum deceleration of a slow car and we consider a v X Final squared equals V X Initial squared plus two ace of ex Delta X. We're trying to find out X again, but again hear the VX initial is going to be 70 miles per hour. We know that we're coming to arrest, so this will be zero we're trying to find out to act so solve. For Delta X, this is going to equal negative. The ex initial squared divided by two times the acceleration in the X direction again. Here, it's not going to be 60. It's gonna be 70 because coming off the ramp, they're going to be going 70 miles per hour. That is the speed of the highway. So it'll be 70 times 16 09 times one divided by 36 100. And then this is squared, divided by two times a negative 1.341 and Delta X is equaling 365 meters. So this would be the off ramp minimum distance for our friend. So this would be the answer for the second part. That is the end of the solution. Thank you for watching

View More Answers From This Book

Find Another Textbook

Numerade Educator

Newton's Laws of Motion are three physical laws that, laid the foundati…

In mathematics, a proof is a sequence of statements given to explain how a c…

Freeway Traffic. According to a Scientific American article (May 1990 ), cur…

Entering the freeway. A car sits in an entrance ramp to a freeway, waiting f…

Entering the Freeway. A car sits in an entrance ramp to a freeway, waiting f…

A car sits on an entrance ramp to a freeway, waiting for a break in the traf…

Engineering a highway curve. If a car goes through a curve too fast, the car…

Highway Design To allow enough distance for cars to pass on two-lane highway…

As a highway engineer, you're asked to design a runaway truck lane on a…

When highway curves are designed, the outside of the curve is often slightly…

Maximum Safe Speed. As you travel every day to campus, the road makes a larg…

A traffic engineer monitors the rate at which cars enter the main highway du…

Speed Limits Studies by the Federal Highway Administration suggest that spee…

CE Predict/Explain On two occasions you accelerate uniformlyfrom rest al…

Along a straight road through town, there are three speed-limit signs. They …

New studies by Federal Highway Administration traffic engineers suggest that…

Constructing a Highway A highway whose primary directions are north-south is…

What's the fastest way to make a U-turn at constant speed? Suppose that…

Automobile traffic passes a point $P$ on a road of width $w$ ft at an averag…

In a stunt being filmed for a movie, a sports car overtakes a truck towing a…

A car is behind a truck going 18 m/s on the highway. The car's driver l…

02:52

A hospital orderly pushes horizontally on two boxes of equipment on a rough …

03:34

$\bullet$ The Kwik-Freez Appliance Co. wants you to design a foodfreezer…

05:44

$\bullet$$\bullet$$\bullet$ A charge $+Q$ is located at the origin and a sec…

03:17

$\bullet$ A steel wire has the following properties:$$\begin{array}{l}{\…

02:31

Human rotational energy. A dancer is spinning at 72 $\mathrm{rpm}$ about an …

02:48

(a) Calculate the buoyant force of air (density 1.20 $\mathrm{kg} / \mathrm{…

03:39

$\bullet$ On-demand water heaters. Conventional hot-water heaters consist of…

08:01

Jumping to the ground. A 75.0 $\mathrm{kg}$ man steps off a platform 3.10 $\…

01:53

$\bullet$ One experimental method of measuring an insulating material's…

01:46

If the bacterium wished to accelerate at a rate of 0.001 $\mathrm{m} / \math…