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The position of a particle as a function of time is given by$x=(2.0 \mathrm{m} / \mathrm{s}) t+\left(-3.0 \mathrm{m} / \mathrm{s}^{3}\right) t^{3}$ . (a) Plot $x$ versus $t$ for time from$t=0$ to $t=1.0 \mathrm{s}$ . (b) Find the average velocity of the particlefrom $t=0.35$ s to $t=0.45 \mathrm{s}$ . (c) Find the average velocity from$t=0.39 \mathrm{s}$ to $t=0.41 \mathrm{s}$ . (d) Do you expect the instantaneousvelocity at $t=0.40 \mathrm{s}$ to be closer to $0.54 \mathrm{m} / \mathrm{s}, 0.56 \mathrm{m} / \mathrm{s},$ or0.58 $\mathrm{m} / \mathrm{s} ?$ Explain.

(a) See solution.(b) $-1.632 \mathrm{m} / \mathrm{s}$(c) $-1.64 \mathrm{m} / \mathrm{s}$(d) Yes

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

Lectures

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So in this problem we have a function that describes the movement of a article which is minus two tea plus three teeth to the power of three. Okay, so first of all, we need to blot graph of the position of the article from the instant TV crew. Zero Open to instance, De Cruz one second. First, we need to discover the final position of the article. Anti Coast one. So let's see. Weren't ecos one The position is going to be minus two. Will Astri says he goes one. And when t co zero, the position is just zeros. That's called the initial position. So before we lost the graph, we must know what is the behavior of 1/3 degree function. So let's put an example in here. Let's see. This is Ah, I'm Axis and this is ah, position access. We know that 1/3 degree function with a positive constant here positive it constantly here is going to be this kind of behavior here. This is the behavior of 1/3 degree function. So, since we are interested in the first part off their movement were interest in this segment in here. We've already know how to plot the graph. So let's do this. We've dysfunction it specifically. We're going to have I did time excess. We're going to have the position access. And here Oh, this is position this this time when the time was one second, We are in the position. One. So the movement off this graph a lot of this graph, it's going to be this one. Okay, so this is the answer for the first heightened. The second item I can be. You want to discover the average velocity off the particle between the times 0.15 open two times judo 0.25 seconds. So, first of all, we need to discover the position of the article in this segments in this instance. But this is going to be miners, too. Uh, times zero point 15 plus three times, little 30.15. So the third degree. Okay, so let's calculated this after carefully this. We know that we are in position manners zero point 29 meters and in the second distance of time, we have acts. Equals minus two time. 0.25. Coolest tree times zero point 25 to the third power. Okay, so this position going to be quote too minus little point 45 meters. So the average velocity between this interval of time, it's going to be doubt X divided by delta t. So this is simply miners, you know, point 45 plus you know, point 29 divided by little 0.25 miners. Your point 15. So what if average velocity is going to be 1.6 minus 1.6 meters per second In the next item Nazi Brighton Sea, we have to calculated again the average lost city. But this time in the interval off time 0.19 open to time 0.21. So that's calculate this. The final position of zero initial position of 0 19 is going to be minus two time 0 19 clothes three times 0 19 to the power of three. So this initial position is going to be minus zero point 36 meters in the final position in 0.21 seconds, going to be minus two times your point went You want those trees? Times zero point went You want to the power of three. So the final position is going to be zero point 39 Minor studio. Dirty knowing meters. So finally, the average velocity it's going to be miners Udo point 39. Plus you're a 0.36 divided by you know 0.21 minor issue of 0.19. This is finally 1.61 minus one point six one meters per second. So respect that the average in the final item respect that the average velocity it's closer to minors 1.62 Because the average velocity we calculated average the velocity it calculated was around 1.6 one meters per second. So it's reasonable to suppose that the velocity and zero point

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