 Ch 1. Particle General Motion Multimedia Engineering Dynamics Position,Vel & Accel. Accel. varyw/ Time Accel. Constant Rect. Coordinates Norm/Tang. Coordinates Polar Coordinates RelativeMotion
 Chapter - Particle - 1. General Motion 2. Force & Accel. 3. Energy 4. Momentum - Rigid Body - 5. General Motion 6. Force & Accel. 7. Energy 8. Momentum 9. 3-D Motion 10. Vibrations Appendix Basic Math Units Basic Equations Sections Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll DYNAMICS - THEORY

Many times, the motion of an object is specified by an acceleration that is constant with time. For example, an object that falls for a short distance in the earth's (or any other planet's) atmosphere experiences a constant acceleration. That constant is written as, ao,

a = dv/dt = ao = constant

By integrating, the velocity can be determined as a function of the acceleration and time, giving v(t) = vo + ao (t - to)

Next, the velocity can be integrated to express the position as a function of the acceleration and time, giving, x(t) = xo + vo (t - to) + ao (t - to)2 / 2

Using the chain rule, the acceleration can be expressed as This relationship can be integrated to express the velocity as a function of the acceleration and position. v2 = vo2 + 2 ao (x - xo)

It should be stressed that above equations are only valid when the acceleration is expressed as a constant.

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