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{}{composition-setup} h4. MIT
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Composition Setup

MIT 8.01

...

Lesson

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4:

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1-D

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Motion

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-

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General

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Lesson

...

Summary

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Excerpt

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We

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consider

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the

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motion

...

of

...

a

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point

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particle

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in

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one

...

dimension,

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which

...

can

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occur

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either

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because

...

the

...

particle

...

is

...

constrained

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to

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move

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along

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a

...

track,

...

or

...

because

...

we

...

restrict

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attention

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of

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one

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Cartesian

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component

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of

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a

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particle's

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motion.

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  In general,

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the

...

force

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applied

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to

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this

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particle

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can

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vary

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arbitrarily

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with

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time.

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  Hence

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the

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particle

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will

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have

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time-varying

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acceleration

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in

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proportion,

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a(t).

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The

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resulting

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motion

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may

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then

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be

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found

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using

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calculus:

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the

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velocity

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v(t)

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is

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the

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integral

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of

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the

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acceleration

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a(t)

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plus

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the

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velocity

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at

...

the

...

start

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of

...

the

...

interval

...

of

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integration.

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  Mathematically

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we'd

...

say

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that

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the

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arbitrary

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constant

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of

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integration

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is

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constrained

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by

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the

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initial

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condition

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on

...

the

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velocity

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.

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  To

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get

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x(t)

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we

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integrate

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v(t)

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and

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add

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the

...

initial

...

position

...

Learning Objectives

By the end of this Lesson, you should be able to:

Introduction

The quantities v(t) and a(t) are important in physics because these mathematically defined quantities appear in experimentally discovered physical laws.  The acceleration is related to the force applied via F=ma, and the velocity determines things like the Doppler Shift and the pressure measured in a Pitot tube - those little bent tubes that stick out of fuselage of an airplane and are bent to face into the airflow so that a pressure-measuring instrument can determine the plane's airspeed.
In our hierarchy of models there are two mutually exclusive special cases: Simple Harmonic Motion caused by a restoring force that varies linearly with the particle's displacement from some center of force, and Motion with Constant Acceleration, caused by a constant force.  Motion with Constant Velocity is a special case of Motion with Constant Acceleration specified by the constraint a(t) = 0.
 

Include Page
Motion -- 1-D General (Definitions)
Motion -- 1-D General (Definitions)
Include Page
Motion -- 1-D General (Cases)
Motion -- 1-D General (Cases)