MIT 8.01 Lesson 4: 1-D Motion - General
Lesson Summary
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We consider the motion of a point particle in one dimension, which can occur either because the particle is constrained to move along a track, or because we restrict attention of one Cartesian component of a particle's motion. |
In general, the
force applied to this particle can vary arbitrarily with time. Hence the particle will have time-varying
acceleration in proportion, a(t). The resulting motion may then be found using calculus: the
velocity v(t) is the integral of the
acceleration a(t) plus the
velocity at the start of the interval of integration. Mathematically we'd say that the arbitrary constant of integration is constrained by the initial condition on the
velocity. To get x(t) we integrate v(t) and add 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.
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| Motion -- 1-D General (Cases) |
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