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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 secondsof its motion? (c) What is the constant speed $V$ that characterizesthe middle portion of its motion?

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

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Cornell University

University of Michigan - Ann Arbor

University of Washington

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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's with negative acceleration. So is decelerating. Okay, so the problem wants us to find the first item. What was the distance? Let's call distance one in their 1st 4 seconds of the movement. The second lighting, the problem wants us to find out. That's called distance three. Off the final ups, that's it'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'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're some up Oh, the area's under the groove. We'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's put too little don'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'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's, um, all the areas we're going to need. We're going. This is going to be equal the total distance. So let's see simplify here it'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'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'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's going to be simply V. So let's see V. It's going to be 4.4 meters and that's the final answer. Thanks for watching so much

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