a-car-in-stop-and-go-traffic-starts-at-rest-moves-forward-22-mathrmmin-80-mathrms-then-comes-to-rest

Question

A car in stop-and-go traffic starts at rest, moves forward 22 $\mathrm{min}$
$8.0 \mathrm{s},$ then comes to rest again. The velocity-versus-time plot for this car is given in FIGURE $2-37 .$ What distance does the car cover in
(a) the first 4.0 seconds of its motion and (b) the last 2.0 seconds
of its motion? (c) What is the constant speed $V$ that characterizes
the middle portion of its motion?

Nathan Silvano · Accepted Answer

Okay, So in this problem, we have a car that covers a total distance off 22 meters in just eight seconds. Ah, As you can see, their movement is described by this figure. We have to three parts of movement, the first part of the movement. The car is accelerating. The second part of the movement, the car is with constant velocity. Any third part of the movement, the car, it&#x27;s with negative acceleration. So is decelerating. Okay, so the problem wants us to find the first item. What was the distance? Let&#x27;s call distance one in their 1st 4 seconds of the movement. The second lighting, the problem wants us to find out. That&#x27;s called distance three. Off the final ups, that&#x27;s it&#x27;s risk rubbed his of the final two seconds of the movement and the sure question, the third I kind of the problem. The problem want us to find out what was the velocity of the meat abortion off the graph. Okay, so first of all, remember that every time we have a graph or velocity vs sign the distance that the object cover in this motion is always the area under the under the curve under the graph, so is numerically identical to the area. So this is the distance. The problem in this particular question is that we don&#x27;t have the velocity. The velocity is the third item we need to discover, as you can see in the graph. So anyway, we know that the total distance the Ark Overs Waas 22 meters. So if we&#x27;re some up Oh, the area&#x27;s under the groove. We&#x27;re going to have first for doubt X one. We have a triangle, as you can see, were few niches for and V. So this area that&#x27;s put too little don&#x27;t going to be 22. This area is going to be four times V, divided by two. So this is going to be bless the second distance. The car travels distance when we have when car have constant velocity, it&#x27;s just going to be a rectangle. Or if they mentions two envy, this is going to be to be plus the last distance the car servers that is a non under triangle, this time with dimensions to on view. So this is going to be to be divided by two. So if it&#x27;s, um, all the areas we&#x27;re going to need. We&#x27;re going. This is going to be equal the total distance. So let&#x27;s see simplify here it&#x27;s going to be to simplify. Here is going to be one. So I have to plus two plus one. This is it was 25 v So answered the third item I can see we have five V equals 22. So we have V equals 22 divided by five. That&#x27;s equals four point for meters per second. This is the answer to the third item. Now that we have, we can simply answer the the item a nd I can be the height and a we want to discover Don&#x27;t, uh, X one as we can see you here doubt X one is defined by two V So is simply to V. Seems we already have the value for V. This is going to be eight point eight meters and the last item I 10 b We want to discover the distance off the less two seconds and the less two seconds. As you can see you here, it&#x27;s going to be simply V. So let&#x27;s see V. It&#x27;s going to be 4.4 meters and that&#x27;s the final answer. Thanks for watching so much

Mayukh Banik · Answer

the past, each other twice. One edge G equals three second, and the second time at Deke was eight second, but be at seven second. We&#x27;re looking at the slope of the two lines and we can see that Lasky off ah, is higher than the velocity. And be because the suburb, the velocity distance time carve is higher for a than for B at seven seconds for part C. When does the cars of saying velocity by looking at the slow being equal? It should be at five second bees always speeding up. So for 2.5 seconds to 12th it has always been speeding up on bees, never slowing down.

Averell Hause · Answer

so at the end of the acceleration period, the velocity, the final would be going the initial velocity which we know to be zero plus the acceleration times t during the acceleration or the time of acceleration. And so this would be equaling 1.5 meters per second squared multiplied by 5.0 seconds and this giving us 7.5 meters per second. Now the this would be the initial velocity for the breaking period. So for part A, we can say after breaking, we can say velocity final equals velocity initial plus the acceleration times the time of the break and so this would be giving us 7.5 meters per second, plus the acceleration of negative 2.0 meters per second squared multiplied by 3.0 seconds, and we have a final velocity equaling 1.5 meters per second. This would be our final answer for part A for part B, Then the total distance traveled. Ah would be equaling essentially the average velocity times T during the acceleration period, plus the average velocity times T during the break in period, so this would be equaling 7.5 meters per second, divided by two most supplied by 5.0 seconds. And this would be plus 1.5 meters per second plus 7.5 meters per second, all divided by two times 3.0 seconds. And we find that then Delta X total is equaling 32 meters. This would be our final answer for part B. That is the end of the solution. Thank you for watching.

Ryan Hood · Answer

party of this question. Ask us to find the average velocity. And so we&#x27;re going to that using this formula we know t to my sti want is ten seconds. But we need to know what x to an ex one is. And we can get that by using the given form of except tea and plugging in appropriate values of teeth. Specifically, we need accept ten seconds and we need exit zero seconds Exit zero seconds is easy. It&#x27;s just you, except ten seconds. We have to remember that being see are these values here. And so we&#x27;re just gonna plug in ten seconds for to hear and then be there and see there and then use a calculator. And once we do that, we get the exit. Ten seconds is equal to one hundred twenty meters. Now that we have these two values, we can use the at average velocity formula here and we get one twenty meters divided by t to my steel want, which is ten seconds. And so the average velocity is kilometers per second onward. To part me, part B, ask us for the instantaneous velocity three different time values to get the instantaneous velocity. We take the derivative of dysfunction. And so we do that by just supplying power law. And we get that the instantaneous velocity would be empty is two times a little b times t just by bringing down the power to its tractor, one from the exponents and then the other term mules three ct squared. Now we know what little being little CR and so if we are given a time value, we could just playing the same and figure out what the velocities are. So we need V of zero point zero seconds and this one is still easy because we just broke into your own zero. They&#x27;re just zero. So we get zero meters. We also need a plug envy of five point zero seconds. It&#x27;s actually do this. We&#x27;LL have to refer back to these two values and again this becomes a calculator problem. And once we play that in, we get fifteen. Oh, by the way, these air meters per seconds because this is bossy and then we need a last one and that&#x27;s me of ten point zero seconds. Playing this and again and using the same being C values we get twelve meters per second. And so now we move on to Percy in part C. We need to know the time value so that the velocity is zero. We know what fifty is. We got a party supplying and zero for me and then solving for tea. Here we have zero equals to be touched. T minus three CT squared. I&#x27;m going to cancel factor of tea and then move the three ct over. We&#x27;re solving for tea, so I&#x27;m going to divide by three c and beings here known Constance. They&#x27;re here whenever we plug them in here. Alof it, too. In the three into our calculator, we get that tea is approximately thirteen point three three, by the way, is repeats forever, and that&#x27;s in seconds. And so approximately thirteen point three seconds after it starts, it comes to rest again. It&#x27;s us, the final answer for Percy, and that&#x27;s the end of the problem. Just

Surjit Tewari · Answer

Could someone be it? The distance covered during the first X elation is is the one using second question of motion. The one is equal to initial lost zero less How you won even is quiet. Stop shooting the values. The one is uh Indo a one. A one has a value of 1.5. The one is by so we will get even. It didn&#x27;t want 75 Meet that this is the value of B one. No, let us find the velocity. Exhilaration one better The acceleration. One place has ended. So this we lost Please everyone equal toe initial lost zero less a one people one is 115 The one is five so even is equal to 7.5 meter. But second, the whole journey can be divided into two parts Here a one is the acceleration and the area to his ex elation. He had lost his 31 their veto And your velocity is zero. So that distance colored during this way, says Deven. And distance over during this place is a little. Now let us find that this tends Tito, they do is equal to initial lost, which is here everyone we want to minus uh So is it plus half a to do you do? It&#x27;s why substituting the values We were only 7.5 He who is three minus, huh? In the 2.1 in two days. What, so doing this? We will get the value of the two. 13 point Zito five made that. So the total bay stands Kevin from initial point, This capital equal to the one less they go, this is equal to 18.75 less. I didn y in Seattle fight. So total distance traveled list even pointed make us. And the velocity after the second phase is Mito B one less a new. This is equal to 7.5 minus 2.1 into a This is equal to 1.2 Meet that What is that good

Ren Jie Tuieng · Answer

No question. We&#x27;re looking at a car whose position can be described. What time? SPT Square minus. C t cute. Well, B is 2.4 and I will see it&#x27;s your point. Went to To find the average velocity. We want to take the total change in the position. Delta X, develop body Total time. You&#x27;re just gonna still talk t total trade you But you should be from X At T equals 2 10 minus x t equals to Syria Everything I just by time off 10 seconds. So mighty close to 10. We started you in Over here you have 2.4. I&#x27;m stent square when you&#x27;re so 0.12 times 10 cubed and four x 20 equals zero This entire, especially serial. So we can you know that by 10 we should get about shelf Meet us plus again. No, your have your finding instantaneous velocity. So the instantaneous velocity We will need two different sheet. Okay, this distance expression your prospective time, So differentiating dept. You get to be t minus tree C t square. And now we can just substitute eat defenders to find healthy a any point in time. So antique rose zero Substituting everything in should get zero right, because both off this Thomas have t insects or multiplying by two serial we get to Manti equals two, five and instantaneously lost years. Just call this fee Times be just 2.4 times five seconds. Minus three times 0.12 times Fight square should get 15 Pieterse for a second. Do the same process But for time And he Yes, it goes to 10 seconds. Centers were give us boat shelf You test per second No, to find how long after starting from rest for our car to come to rest again means we want the instantaneous velocity to be zero and we will not consider t equals zero s The answer Mangement is evil. We have either very effective isil t right There&#x27;s two different possible. And since one is t equals zero, which is the one that we already know and the other one would be And this fact over here is cereal. Two big ones too. She c t so tease was too to be over three c have you will get 13.3 seconds

Problem

A car and a truck are heading directly toward one…

Problem 63 Hard Difficulty

Answer

(a) 5$\cdot 2 m$
(b) 2$\cdot 6 \mathrm{m}$
(c) 4.4 $\mathrm{m} / \mathrm{s}$

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(a) 5$\cdot 2 m$(b) 2$\cdot 6 \mathrm{m}$(c) 4.4 $\mathrm{m} / \mathrm{s}$

Physics

Elyse G.

Andy C.

Liev B.

Marshall S.

Math Review - Intro

Algebra - Example 1

James S. WalkerPhysics

Elyse G.

Andy C.

Liev B.

Marshall S.

(a) 5$\cdot 2 m$
(b) 2$\cdot 6 \mathrm{m}$
(c) 4.4 $\mathrm{m} / \mathrm{s}$

James S. Walker

Physics