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Numerical/Computer $*$ 95. (II) The Table below gives the speed of a particular drag racer as a function of time. (a) Calculate the average acceleration $\left(\mathrm{m} / \mathrm{s}^{2}\right)$ during each time interval. (b) Ascribing numerical integration (see Section 9 of Describing Motion: Kinematics in One Dimension) estimate the total distance traveled $(\mathrm{m})$ as a function of time. [Hint. for $\overline{v}$ in each interval sum the velocities at the beginning and end of the interval and divide by $2 ;$ for example, in the second interval use $\overline{v}=(6.0+13.2) / 2=9.6 ]$ (c) Graph each of these. $t(s) \quad 0 \quad 0.501 .001 .502 .002 .503 .003 .504 .004 .505 .00$ $v(\mathrm{km} / \mathrm{h}) 0.06 .013 .222 .332 .243 .053 .5$ 62.6$\quad 70.678 .4 \quad 85.1$

(a) The average acceleration for each interval is calculated by $a=\Delta v / \Delta t,$ and taken to be theacceleration at the midpoint of the time interval. In the spreadsheet, $a_{n+\frac{1}{2}}=\frac{v_{n+1}-v_{n}}{t_{n+1}-t_{n}} .$ The accelerations are shown in the table below.(b) $x_{n}+\frac{1}{2}\left(v_{n}+v_{n+1}\right)\left(t_{n+1}-t_{n}\right)$(c) see graph

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 Washington

Simon Fraser University

University of Winnipeg

McMaster University

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…

Distance from velocity dat…

The table shows the positi…

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A test driver at Incredibl…

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The table shows speedomete…

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Figure $\mathrm{P} 2.26$ r…

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Acceleration A drag racer …

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Figure $\mathrm{P} 2.24$ r…

so here for part A, we can say that the average acceleration for each interval would be calculated by the average acceleration equaling Delta V divided by Delta T on. And we can say that, uh, and this is going to be taken to be the acceleration at the midpoint of any time interval. So we can say in the spreadsheet, we can say that a to the end plus 1/2 would be equal to B to the n plus one minus v to the end, divided by t to the n plus one minus t to the end. And so oh, um, we can Ah, the second workbook has the accelerations. However, this would be the the except the formula that you were going to use for part a four part B. However, we need the position at the end of each interval and this could be equal. This would be act to the end, plus one to the next interval. Bess essentially would be equal to the initial position at the interval, plus 1/2 times V to the end plus V to the N plus one to the next velocity in the ER data set and then t to the end plus one again minus teach the end. And this we can also represent this as X would be equal to X initial, plus the average velocity times out to tea. However, you want to use this equation because this is much obviously much more specific and tabulated. It would look like this. So these would be the time with the average with the velocity and kilometers per hour and the velocity and meters per second again, we know that one meet one meters per second is gonna be 3.6 kilometers per hour and we know here it would be thine seconds. So this would be, um, for A and these would be for B and then for part C, they wanted to use to grasp the um they want you to go out the acceleration versus time and the distance versus time. And these are what the grafts would look like. You could simply put the data set into excel and then obtain a graph that way. That is the end of the solution. Thank you for watching

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