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(II) A space vehicle accelerates uniformly from 65 $\mathrm{m} / \mathrm{s}$ at$t=0$ to 162 $\mathrm{m} / \mathrm{s}$ at $t=10.0 \mathrm{s} .$ How far did it movebetween $t=2.0 \mathrm{s}$ and $t=6.0 \mathrm{s} ?$

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$4.2 \times 10^{2} m$

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

University of Michigan - Ann Arbor

Hope College

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.

05:04

(II) A space vehicle accel…

0:00

01:19

If a vehicle accelerates…

03:40

A "rocket car" i…

03:14

A car slows down with an …

03:29

(II) A sports car moving a…

01:53

A car accelerates uniforml…

03:03

Deceleration A car slows d…

00:41

A car traveling at $+7.0 \…

02:10

(I) A car accelerates from…

03:39

(II) Determine the stoppin…

01:09

Starting from rest, an aut…

Now we have ah space vehicle and it's accelerating from 65 meters per second 262 meters per second. It's going from zero seconds time to 10 seconds time. And we want to know how far travels from T equals two t equal six. And in order to do that, I'm just gonna figure out it's position at those two points and that I could find the displacement between. So first I want to find the acceleration. Um, And to do that, I can say that my V is gonna be be zero plus 80. And so this is my B zero and this is my V. This is okay, So V is 162. B zero is 65 and our total time is 10 seconds now. My soul for a So this is 97 equals 10 A. So a equals 9.7 meters per second squared. And now to find the displacement from two seconds to six seconds, I can say that my position at any time T is my initial position plus B zero t plus 1/2 A T squared. OK, so I'll do my position in two seconds in my position at six seconds, it's my position. At two seconds is going to be zero were starting at zero, no matter what. Uh, initial velocity is 65 I'm going to two seconds and 1/2. I know my acceleration is 9.7 and two squared. And this one, it's gonna be again. Zero Sam, initial velocity different time. Now we have six seconds and 1/2. 9.7 six squared. OK, let's find out Two seconds first. So this is gonna equal 149 0.4 meters. That's my absolute position. And this is 564.6 meters. And so if I want to find my Delta X, it's gonna be ex of six minus X it too. So this is going to be 564.6 minus 149.4. That's gonna give us 415.6 meters, which is about 4.2 times 10 squared meters. And that's our displacement from a time of two seconds to a time of six seconds during the acceleration

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