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Question 1710 ptsTwo trains are moving along track toward each other when they each begin t0 slow down. The velocity versus time graphs for the two trains are shown...

Question

Question 1710 ptsTwo trains are moving along track toward each other when they each begin t0 slow down. The velocity versus time graphs for the two trains are shown in the figure: Train A is the solid, orange line; and train B is the dashed; blue line: The graphs begin when the trains are separated by 200 m and end when each train comes to complete stop.Train BTrain A40 30 1 20 10 0 -10 ~20 330Time (s)What is the acceleration of train A, in m/s?? B. The initial position of train B is 200 m. Find

Question 17 10 pts Two trains are moving along track toward each other when they each begin t0 slow down. The velocity versus time graphs for the two trains are shown in the figure: Train A is the solid, orange line; and train B is the dashed; blue line: The graphs begin when the trains are separated by 200 m and end when each train comes to complete stop. Train B Train A 40 30 1 20 10 0 -10 ~20 330 Time (s) What is the acceleration of train A, in m/s?? B. The initial position of train B is 200 m. Find the equation for the position of train B as a function of time. (i.e. Find I = To Vort + {0z0) When each train has come to a stop; how far apart are the two trains; in meters?



Answers

The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track ($\textbf{Fig. P2.62}$). The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/s$^2$ in a direction opposite to the train's velocity, while the freight train continues with constant speed. Take $x =$ 0 at the location of the front of the passenger train when the engineer applies the brakes. (a) Will the cows nearby witness a collision? (b) If so, where will it take place? (c) On a single graph, sketch the positions of the front of the passenger train and the back of the freight train.

This question. Okay, so you have a passenger train that is moving into the right. Okay, Uh, at an initial speed of 25 m per second. Okay. And then someone spotted a freight train. Hey, that's moving at 15. Because second entire meters in front. So the engineer steps on the break, and we want to find out the two trains collide, and if so, where would it happen? And we need to draw that, uh, position time grabs. Okay. For the I send your train and the free train. Okay. Okay. So to solve this problem. So this is a one deacon automatics problem. Uh, so for party, uh, will be using, uh, X equals two x, not plus, you know, e plus half 18 square he to write down the position of the front of the passenger train and the back of the fridge drinking. So X p is the for the passenger. So, uh, so the front starts from X equals zero. So it's not zero for passenger. So just to uh huh yeah, mhm for the passenger train. So X p is, uh, zero class. You know, T, which is 25 t and then the is negative have times negative. One piece. Where? Okay, then. So it's simplified. You get 25 t minus 0.5 T square and then for the free chain. Okay, so x f s excellent is 200 and we know is 15 p. There's no acceleration for the preaching. Okay, so I suppose yourself, uh, I suppose if you want to find out if they collide, you assume First assume that they collide to find the time it happens all the time Have There's no sense about time for the collision to occur. Then the collision will not take place. If we found that there is a positive t that or the collision will take place, then collisions will occur. So suppose the trains collide we then X p equals two x f. So this is what we are going to write. 200. Last 15 Key equals to 25 t, then still going through five T square. Yeah, your points are fighting the square minus and t last 200 because 60 Okay, so using the quadratic formula, he is. And that's my left hand square minus four times 203.5 Then square and then divide by 0.1 is calculated t to be 177 seconds and all. 22.5 seconds. Okay, so, uh, he is positive. So, uh, which means the two trains. Well, can I? Yeah, the first collision, uh, the client And he goes to 22.5 seconds. Okay, so the answer. Yes, it will collect. Okay. In their client T versus 22.5 seconds. So this is the ground for pussy and use it. Okay, so in part B. Okay, so where will the collision take place? Uh, so we'll find using. Except he goes to 200 5 15. Key the collision. Please explain that. Yeah. He goes to 22.5 seconds and x f is equal to 200 plus 15 times 22.5. And this is 588 m. Okay, so, uh, the collision takes place. Collision takes place, right. Exit goes to 508 m. Ah, from the origin. Yeah, right. Then for policy, you want to sketch the positions of the front and passenger train in the back of the free train. Okay, so this is the answer for Patsy. He saw the blue car is a freight train, And, uh, and the great Green Coast is the passenger train. Yeah. So, uh, you see that? Yeah. This is 22.5 seconds. Thank you. Is our 177 seconds. Hey. This? Yes, A continue emotion. Mhm. Uh huh. On parallel trick tracks. Yeah, of course. In this case that we have only had a single track. So the 22.5 seconds the answer. Okay, Right. So that's all for this question.

The question I have a dream that is moving At speed 24 m/s in the stop direction. The theme applied a break for nine seconds And his feet after those 9, 73, 6 m for a second. This happened over the course of nine seconds as a sad Were asked to 1st draw a velocity graph of the train starting two seconds after the brake has been applied and extends to 1 2nd after the break has ended. So that's great. Now we know that in order to do this, we will need to specify the points. So here is the graph, there is the graphing area and I'll decide to look. Of course we have the time on the horizontal axis. Let's start at 1 to freedom. Four 567 8, 9, 10, 11. Finally, 12. And we go force here for eight, 12, 16, 20 and 24 28. Okay, so first of all, for two seconds before the break has been applied. I assume that the train was moving at simply constant velocity with 24 m/s. But here is something that we have to be very careful about it because in the question it says that let's assume that the X axis points to the north and here we're doing the VFX. So if the train was moving with 24 m/s in the South Direction, then according to protection, This is -24, So that's negative 24 And this will be negative six as well. So now we're ready to start out graphing, we'll start that 24 and we'll keep this for two seconds. We're just constant velocity. So this is the first two seconds. Now we need to specify the ending point. So after nine seconds, This makes it at this second number 11, The speed was six. So basically that's the four. Yes, that's halfway. Yes, So that's almost here. 11, 12. Okay, Offly will connect those two points because the exploration we'll assume the exploration is constant as well, Not changing during the nine seconds themselves. So that's how the velocity graph looks like during the nine seconds. And finally when the brakes stopped It will keep moving at Madison Velocity Out six. Severe. We assume that we are at six. Okay, that's great. So that's the graph being were asked to calculate the exploration of the train in that period. And that's very easy because we know that the excavation is just equal to the change in velocity divided by the change in time. In here our velocity changed from or change it to negative six. And originally it was negative 24. So that's minus minus, gives us plus 24 Divided by nine seconds. So that's 18 divided by nine. And the excavation is two m per second squared. And it is positive because the exploration in that case will point in the north direction because it's trying to stop the train. So its opposite to the trains motion which is originally in this south direction. Finally, we're asked to catholic, How much distance did the train travel during the nine seconds. That's pretty straightforward. If we apply the equation X is equal to lead up taking plus half. Oh, he squared. I'm pretty sure you're familiar with right? And we will substitute now. But just we need to be careful about this time convention. Will you use here? So v. negative 24 And the dome is nine seconds plus half, multiplied by two, multiplied by knowing square Did this on your calculator, you'll have negative 135 meters. And this negative sound here indicates that the train is moving in the south direction, even if it's decelerating or it's losing velocity, but it's it is still moving in the south direction, and it has moved already, 135 m, counting the absolute value, like to count the distance that I've traveled, So 135 m south.

So the displacement Delta X is equal in the area under a velocity versus time graph because, of course, the area or the the displacement for each train, it's simply the integral of the velocity again, with respect to time. So we can say that here, each area is trying is triangular, and so the absolute value of the displacement. For one train, you can say the first train. This would be the total absolute value of the displacement is equaling, 1/2 multiplied by 40 meters per second, multiplied by five seconds, and this is giving us 100 meters now for the second train. The absolute value of the displacement would be equal in 1/2 times 30 meters per second, most supplied by here four seconds and this is giving us 60 meters. The initial gap was 200 meters and then the gap has been narrowed by 160 meters. So essentially the new separation is 40 meters. That is the end of the solution. Thank you for watching

Hello, students in this problem, we have given a train is moving between two stations station one hair and a station to here. And we have given their four point a B c and be And the distance between these points is equal. I suppose that distance is equal to be between these points and then is a starting with an initial is 50 I suppose from point A to B, it takes time, p and from me to see it takes time t time and from point C two d Suppose it takes t devil frame right now we know that according toe can dramatic equation as is equal to UT plus half It is square, I suppose, from point A to B, it has a X elation A in this direction and from B to C. It has no ex elation without because it is moving with a constant velocity. Suppose this velocity is we. And from C to D, it is d X listing with the same magnitude off exploration in this oppose it direction. So from point A to B according to s is equal to utilize Harvey Half 80 square. We can say the will be equal to U is zero. So this will be called a half a T squared. This is a question one now from me to see we can write. They will be equal toe V into T deaths. Now we can find this velocity. This will be equal to you. Pless, 80 u is zero. So this velocity will be equal to aid duty. So from here we can write. This distance is equal to 80 into Peter's. Suppose this medication number two now from point C two d Suppose it takes time t develop prime so we can write. And we know that final velocity is zero here and the initial velocity is V so we can write. We finalize ical toe the initial plus A and duty double time From here we know that final velocity is zero and the initial is a called a V And here the ex elation is in the opposite directions like take negative here. So from here we can write t double time will be called to Viv. I and we know that velocity of V is equal to 80. So from here we can say t double prime is a call to duty, right? So we can say it takes total time T plus teach brown plus t double prime is a call to five minutes. So we can try t. This will be called toe booty. Plus t time will be called +05 This is a question number Third. Now we will create the question number one and to education. Nobody is One is half a T squared. Any question Number two is 80 into people From here we can write. The crime will be called Toe B. Bye toe mate. No supposed vacation number four. We will solve vacation number three and forth from TV and four we can say to people us TV I too should be equal to five. From here we can write. He will be equal to two minute do you and tea time will be equal toe the right to it means one a minute. So we can say finally from point A to B, it takes two minutes from B to C. It will take one minute and from C to d, it will take again. Dominate


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