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(II) The position of a racing car, which starts from rest at $t=0$ and moves in a straight line, is given as a function of time in the following Table. Estimate $(a)$ its velocity and $(b)$ its acceleration as a function of time. Display each in aTable and on a graph.$\begin{array}{lllllll}{t(s)} & {0} & {0.25} & {0.50} & {0.75} & {1.00} & {1.50} & {2.00} & {2.50} \\ {x(m)} & {0} & {0.11} & {0.46} & {1.06} & {1.94} & {4.62} & {8.55} & {13.79} \\ \hline\end{array}$$\begin{array}{rrrrrrrr}{t(s)} & {3.00} & {3.50} & {4.00} & {4.50} & {5.00} & {5.50} & {6.00} \\ {x(m)} & {20.36} & {28.31} & {37.65} & {48.37} & {60.30} & {73.26} & {87.16}\end{array}$

a) $10.48 \mathrm{m} / \mathrm{s}$b) $5.32 \mathrm{m} / \mathrm{s}^{2}$

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

University of Michigan - Ann Arbor

University of Washington

Hope College

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.

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(II) The position of a rac…

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(III) The position of a ra…

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A race car moves such that…

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The position of car is giv…

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10:22

The position of a car in a…

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The table shows the positi…

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[T] The position in feet o…

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The velocity-versus-time g…

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The position of a car as a…

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Numerical/Computer $*$ 95.…

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The position $s$ of a car …

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Use the velocity-versus-ti…

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for this problem were given position and time data for ah, race car and we want to find the velocity as a function of time. In the exploration is a function of time and the way I'm going to do that, I'm just gonna use numerical differentiation and excel to make this really quick. So if we want to find a given velocity to do Delta X over Delta T, we take the position one at 11 greater position and one less position that interval and divided by the changing time over that same interval. And we do that all the way down for each value until we get to hear and for the last one, we don't have anything in these spots. So every time you do numerical differentiation, you're going to lose the edge values. Except we also know that the race car starts at rest. That's what we're given in the problem. So I just plugged in zero there. Then we can do the same thing for the acceleration. Just take the difference of the velocity and divided by the time difference and do that all the way down. And now we get our approximate values for velocity and exploration at each time and that if we want to graft these, this is what it looks like. The velocity. It's pretty linear, Um, of you. It's hard to say exactly what it is, but it looks linear from the broad perspective, and I want to be getting to acceleration and we can see it. Actually, it's the subtle changes in velocity or magnified. Um, but what I'm doing for these graph is just graphing these columns. So velocity versus time, acceleration versus time. I'm just graphing those values, and that's what I that's what it looks like.

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