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 Fluids Math Mechanics Statics Thermodynamics Author(s): Kurt Gramoll ©Kurt Gramoll

 DYNAMICS - CASE STUDY SOLUTION Train Motion When integrating the acceleration to determine the velocity and position, the initial conditions must be specified. The lower limits of integration will be      vo = 50 m/s      to = 2 s When the acceleration is integrated, the expression for the velocity, as a function of time, becomes                   = t2 + 46      v(t = 4) = 62 m/s The next step is to integrate the velocity. However, it is important that v(t) is integrated and not the velocity at 2 seconds, 62 m/s. This is a common mistake. Integrating the velocity function, v(t), gives an expression for the position as a function of time,                   = 0.333 t3 + 46 t - 94.67      x(t = 4) = 110.7 m Note that the initial position xo was set to zero when to = 2 so that the equation for x(t) gives the change in position starting at t = 2.

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