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(II) Given $v(t)=25+18 t,$ where $v$ is in $\mathrm{m} / \mathrm{s}$ and $t$ is in s,use calculus to determine the total displacement from$t_{1}=1.5 \mathrm{s}$ to $t_{2}=3.1 \mathrm{s}$

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$106 \mathrm{m}$

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

Rutgers, The State University of New Jersey

University of Sheffield

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 here the we confined the displacement by finding the integral of the velocity over the given time interval. So you can say that the formula for the displacement would be equal to teach someone to integrating from t someone to teach up two of the velocity equation with respect to time. And so this would be equal to 1.5 seconds to 3.1 seconds. Uh, Times 25 plus 18 tee times. D t um, this is going to be Delta X is going to be equal to 25 t plus 90 squared, evaluated at 1.5 seconds and 3.1 seconds. And so we can say that Delta X it is going to be equal to 25 times 3.1 plus nine times 3.1 squared minus 25 times 1.5 uh, plus nine times, 1.5 quantity squared, and we find that Delta X is going to be equal to approximately 106 meters. This is our final answer. That is the end of the solution. Thank you for watching

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