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MIT 8.01
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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
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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 |
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of |
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a |
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in |
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one |
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dimension, |
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which |
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can |
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occur |
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either |
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because |
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the |
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particle |
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is |
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constrained |
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to |
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move |
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along |
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a |
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track, |
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or |
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because |
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we |
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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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the
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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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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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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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a(t)
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plus
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the
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at
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the
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start
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of
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the
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interval
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of
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integration.
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Mathematically
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we'd
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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
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the
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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
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initial
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.
Learning Objectives
By the end of this Lesson, you should be able to:
- Read and understand the One-Dimensional Motion (General) model summary.
- Accomplish the Learning Objectives listed in that summary.
- Summarize the structure of the Hierarchy of models that fall under the One-Dimensional Motion (General) model, and state the specializations required for each sub-model to apply.
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.
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