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The velocity-versus-time graph for an object moving in a straight line is given in FlGURE $2-45 .$ (a) What is the acceleration of this object? (b) If this object is at $x=12.0 \mathrm{m}$ at time $t=0,$ what is its position at $t=1.00 \mathrm{s} ?$ (c) Assuming the acceleration of theobject remains constant, what is its position at $t=5.00 \mathrm{s?}$

(a) $a=4 \mathrm{m} / \mathrm{s}^{2}$(b) 14.5 $\mathrm{m}$(c) 64.5 $\mathrm{m}$

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Cornell University

Rutgers, The State University of New Jersey

University of Sheffield

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Okay, so and this problem, we have, Ah, the lawsuit versus time graph. And as you can see, the ending velocity is just That's sports in here is just 4.5 there. Ending time of the movement of your object is just one second. The beginning of velocity is 0.5 and zero off time. Okay, so what? The problem? Once the first item, we need to discover the average velocity off the this object. So we need to discover the lost city. Well, we know that average velocity is defined as the difference in velocity average. Sorry, Average acceleration. We need to discover acceleration. So we know that the average acceleration is defined the difference in velocity divided by the difference in time. So Okay, look into the graph. We know what is the final velocity, and they need your velocity. So I was just going to be 4.5 miners, 0.5 divided by one, which is the total time. So the acceleration that we want to discover is just for meters your second square. This is the answer to the first item. The second item. What we want to discover in the second item and the second item. The problem say's that the object begin his movement at a position of 12 meters and he wants to discover the position of the object after one second. Okay, so since we already have velocities and we want to discover the position we can use, uh, equation off velocity as a function off position. So here we have the final velocity in one second is just 4.5 square equals Thio Danish a velocity, which is 0.5 square was two times four. Don't, uh X. So this is going to be equal. 20 point 25 gross. Zero points. 25 plus eight out X. So this is going to be Let's see, doubt the axe Eve close 20 divided by eight, which are 2.5 meters. But the answer to the second item he's going to be the final position, which are we want to know is 12 which are the initial position plus the difference. So I was going to be 14 0.2. Sorry. 0.5 for teeth point five meters. Okay, so this is the second light and the third eye tonight. I didn't see We want to discover what is the position of the object knowing that the separation begin, Constance. So we want to know position after five seconds? No, in desperation is the same. Okay, so now we can use the position of the object as a function off time because it is easier. We don't know the final velocity, so we can use the velocity as a function of position two. No, there's not. Just through here was Hey, do you square divided by two. Okay, so the final position we want to discover going to be initial position. Trout Initial velocity, 0.5 times five seconds. Bliss four point five. Divided by two times five square. Richard, 25. So during this calculation, we're going to find that the final position. 64 0.5 64. Boring five meters. And this is the final answer.

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