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(I) A rolling ball moves from $x_{1}=3.4 \mathrm{cm}$ to $x_{2}=-4.2 \mathrm{cm}$during the time from $t_{1}=3.0 \mathrm{s}$ to $t_{2}=5.1 \mathrm{s} .$ What is itsaverage velocity?

$-3.6 \mathrm{cm} / \mathrm{s}$

Physics 101 Mechanics

Chapter 2

Describing Motion: Kinematics in One Dimension

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

University of Sheffield

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

02:31

(I) A rolling ball moves f…

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A rolling ball moves from …

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Suppose that a ball is rol…

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01:46

The acceleration (in $\mat…

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this's Chapter two problem for in this problem, we're given a starting and ending position for a ball and were also given a starting and ending time. And we're looking for an average velocity. Well, we know average velocities that's going to be you generated. His V bar is equal to our change in position or, in other words, our displacement divided by our change in time or the time interval that's elapsed. So we find the change in distance and the change in time. We confined our average velocity and were able to find both those values. So using the starting and ending positions, we can get our change in position. Bye. Subtracting our initial position from our final position since are all started at a positive position and went to a negative position. We expect that our change of position is going to B negative, and indeed it is. You subtract those two and you get minus 7.6 centimeters and then even do basically the same thing for the time interval. So if we want our change in time delta t we take our final time t too, and subtract our initial time t one and we expect to get a positive value here because, as always, time moves in the forward direction. Make that Mina sign clear. And so here we've got 2.1 seconds. All right, so you plug that in for Delta T. Well, you're minus seven 0.6 centimetres in for Delta X. You divide the two. You've got some centimeters divided by some seconds. So we expect our answer to be in centimeters per second and you end up with minus 3.6 centimeters per second. And so that is our average velocity as requested notice the difference here between average velocity and average speed Is that average speed, greed The magnitude of this so would be positive, 3.6 centimeters per second. But since we're looking for average velocity, we need to also know the direction. And here, moving in just one dimension direction is in a feud by a positive or negative sign. So it's that negative sign there that tells you the direction of your average velocity, which is what we want

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