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

A fugitive tries to hop on a freight train traveling at aconstant speed of 5.0 $\mathrm{m} / \mathrm{s}$ . Just as an empty box car passeshim, the fugitive starts from rest and accelerates at$a=1.2 \mathrm{m} / \mathrm{s}^{2}$ to his maximum speed of 6.0 $\mathrm{m} / \mathrm{s} .$ (a) How long does it take him to catch up to the empty box car?(b) What is the distance traveled to reach the box car?

a) $t_{\text {total}}=15$ seconds it took for the fugitive to catch up to the train.b) $x_{\text {total}}=75$ meters the fugitive traveled to reach the box car

Physics 101 Mechanics

Chapter 2

Describing Motion: Kinematics in One Dimension

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rutgers, The State University of New Jersey

University of Washington

University of Sheffield

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

04:08

A fugitive tries to hop on…

03:26

06:53

(III) A fugitive tries to …

03:15

02:28

A car moving at 50m/s slow…

01:25

A drag racer starts her ca…

02:22

A state trooper is traveli…

02:40

The driver of a pickup tru…

01:32

A car moving along a strai…

01:41

Freight trains can produce…

04:05

03:04

The driver of a car travel…

01:28

04:52

Two subway stops are sepa…

we have a train that's going at five meters per second. And as it passes a fugitive, he's going to accelerate to try to catch up to the train at 1.2 meters per second squared. And we were looking for how long it takes him to catch up to the train both in terms of time and distance. So first of all, we know that you can only reach a speed of six meters per second. So to start off, I'm gonna figure out how long it takes them to do that. We know that his velocity is gonna be his initial velocity plus acceleration times time. We know this velocity starting at rest and we console for time. So it takes him five seconds to reach his max. Speed Clear s Oh, now I can I can figure out how long or how far he goes in this time with B zero T plus 1/2 A T squared and our velocity zero. We know our acceleration is 1.2 and the time is five seconds that we found in the last part. So his horizontal displacement in this time it's gonna be 15 meters now the train. This is the fugitive and the train. In the same time, we have Delta X, this V zero t what's 1/2 A T squared? The train has no acceleration. So this term doesn't matter and we get our delta X for the train is its velocity five meters per second times five seconds. So I don't The X for the train is 25 meters and now we can create an expression to solve for the time it takes for the fugitive to catch up to the train using this information. So we know are adults x for the fugitive is going to be this initial position 15 meters and it's the position. I'm just gonna set an equation after I've already sold for how far he goes while he's accelerating and then after it's not accelerating going in a constant velocity, it's much easier to figure out the time. Yes, we have 15 and then plus we're going to Sierra velocity times. Time is our displacement beyond that, So his, uh, displacement is gonna be 15 plus we always going at six meters per second times time and for the train trans Delta X is gonna be 25 is its position. Once the fugitive reaches his maximum lot are yet Max velocity and we're gonna add on VT. So the train's position is 25 plus five meters per second time's time and these Delta X for the train and the fugitive we want to set equal because we're trying to figure out when the fugitive catches up so we can say 15 plus six. T is 25 plus five t and we'll bring the tea over this side and the 15 over to this side. So we get ah, 60 minus five. T equals 25 minus 15. And so our tea is 10 seconds. Yeah, and this is the time that it takes for the fugitive to catch up to the train after he has already reached. Ah, his max velocity of six meters per second. And the time it took to get to that velocity was five seconds. So are a total time. He's gonna be 10 seconds plus five seconds. It's 15 seconds from when the boxcar passes the fugitive. Okay, that's the total time it takes. Now we want to find how far how far he has to run And for this I'm just gonna plug in the time into ah, the expression for the trains distance. Which is much easier because I don't have to worry about acceleration term. So the trains displacement. It's just V t. And this displacement is five meters per second. Okay, for a total time of 15 seconds, and so are adults x 75 meters. And that's how long the fugitive has to run to catch up with the train.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:40

An airplane has a length of 60 $\mathrm{m}$ when measured at rest. Whent…

01:24

What is the speed of a particle whose kinetic energy is equalto (a) its …

05:15

(II) A baseball is seen to pass upward by a window 23 $\mathrm{m}$above …

03:41

A sample of the radioactive nuclide $^{199} \mathrm{Pt}$ is prepared that ha…

01:05

(1) A $650-N$ force acts in a northwesterly direction. Asecond 650 -N fo…

07:15

Water discharges from a horizontal cylindrical pipe at the rate of 465 $\mat…

03:03

(II) A falling stone takes 0.33 s to travel past a window2.2 $\mathrm{m}…

10:15

In the design of a rapid transit system, it is necessary to balance the aver…

01:39

. Two long current-carrying wires run parallel to each other. Show that if t…

02:08

(II) A skier moves down a $27^{\circ}$ slope at constant speed. Whatcan …