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An object moves along the $x$ axis. Figure 2.43 shows a graph of its position $x$ as a function of time. (a) Find the average velocity of the object from points $A$ to $B, B$ to $C,$ and A to $C .$ (b) For the inter-A to $C .$ (b) For the inter-$A$ to $C .$ (b) For the intervals in part (a), would the average speed be less than, equal to, or greater than the values you found in that part? Explain your reasoning.

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Physics 101 Mechanics

Chapter 2

Motion along a Straight Line

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

Hope College

University of Winnipeg

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Okay, so here we have t of at a tea at B and he had seen this is equaling zero seconds, 3.0 seconds and 6.0 seconds respectively. And we also have facts that a X at B x at sea This is equaling zero meters, 25.0 meters ands, aerial meteors, respectively. So for part A when we want to find the average velocity, it's simply going to be Delta X The fight. If I tell tha t eso when we want the average velocity from a to B, we get the this the displacement of B minus displacement at a divided by the time a bead right about minus the time, eh? And this will be 25 divided by TB modesty A would be three and this would equal 8.33 meters per second. And so we want to find the average velocity from B to see. We have the position at C minus the position at be divided by the t it seem honesty. It eh? And this is again Ah, not 25 over three, but negative 25 divided by six minus three. And this is again negative 8.33 meters per second velocity from A to C. This would be the exposition at C minus, the exposition at a divided by t of seem honest Eva now the denominator. Six. However, the change and displacement is equal to zero. So this was simply be zero meters per second and then for part B, it's asking us, Ah, would the speed change so essentially, for the A B. The magnitude of the displacement equals the total distance traveled, so that would be correct. So for a va bien, we can say that Ah, total distance traveled equals magnitude of displacement. Speed would be equal to B A p. Now for a beast, enough for the velocity. Fbc Again, the total distance traveled would be different than the magnitude of displacement, and speed is also always positive. So for BBC, this speed would be greater than BBC and the speed would also be greater. Rather, we can say speed is greater than cereal greater than BBC. And then for finally the see well, this is simply this is simply equal to zero because the displacement of zero, however, the speed doesn't measure displacement that measures total distance traveled again. So for V A. C. Um, for the third case, we can say that speed would be greater than zero and, of course, greater than the sea. So that would be for the first case, the second case and the third case. That's the end of the solution. Thank you for watching.

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