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A subway train starts from rest at a station and accelerates at a rate of 1.60 $\mathrm{m} / \mathrm{s}^{2}$ for 14.0 s. It runs at constant speed for 70.0 $\mathrm{s}$ and slows down at a rate of 3.50 $\mathrm{m} / \mathrm{s}^{2}$ until it stops at the next station. Find the total distance covered.

1800 $\mathrm{m}$

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

Simon Fraser University

Hope College

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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So we're trying to find the total distance covered and we have a couple. We have three scenarios here. So we have Ace of one equals 1.6 amuse per second squared and this occurs T someone equals 14.0 seconds. So for the 1st 14.0 seconds, there's an acceleration of 1.6 meters per second. So let's find Delta X one first Delta X the distance traveled during this time interval. That'll be VX initial T plus 1/2 80 squared. We know that VX initial is zero and this is going to be equal to 1/2 times 1.6 times 14 squared. And we have delta X of one equaling 157 meters. Now let's find the final velocity of this. The X final is going to be equal to 1.6 times 14 and this is equal in 22.4 meters per second. So keep this. Keep this final velocity because this is going to be your initial velocity starting the second scenario. So after this, we then have a constant velocity for Delta. T two equals 70 seconds. So for 70 seconds, you're cruising at 22.4 meters per second and you're not accelerating. So we can say Delta X two would be equal to the ex initial t plus half a T squared again. There isn't an acceleration, so I'll be zero and we have VX initial, which would be fi X final from the first scenario. Sorry, 22.4 times t of 70 seconds. And we're getting that Delta X sub two equals 1,560 eh meters, So this would be your second scenario. Now, for your third scenario, we have a a sub three equaling 3.50 meters per second squared. And we know that the X final equal zero. So here were actually coming to arrest with a deceleration of 3.5 meters per second squared. So we can say that the X final squared equals V X initial squared, plus two times a sub ex Delta X sub three Ah, and actually will say some threes. Well, for this case of three and so we know that VX final is going to be zero. So we can say that Delta X sub three is going to be equal. Teo Negative 22.4 squared the initial velocity from the previous the final velocity from the previous scenario and then divided by two times the acceleration. So two times negative 3.5 and this is get this is ah giving us 72 meters. So essentially, when we're trying to find x total, we have 157 plus 1,568 plus 72. And this is giving us a total displacement of 1,797 meters. So this would be our final answer. This would be our total ex displacement. That is the end of the solution. Thank you for watching.

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