Ch 1. Particle General Motion     Multimedia Engineering Dynamics
Position,
Vel & Accel.		 Accel. vary
w/ Time		 Accel. Constant Rect. Coordinates Norm/Tang. Coordinates Polar Coordinates Relative
Motion		  
Dynamics
 Line Motion: Acceleration with time Case Intro Theory Case Solution Example
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 6. Force & Accel.
 7. Energy
 8. Momentum
 9. 3-D Motion
 10. Vibrations
 
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DYNAMICS - EXAMPLE
    Example

Car Acceleration 		 

The acceleration of a car over time is know as a(t) = (2t2 + t) m/s2. Assuming the car starts from rest, how far does the car travel in 5 seconds?
   
    Solution


Car at t = 0 and t = 5 seconds.

 

Since distance is needed, the acceleration equation must be integrated twice. First, find the velocity function,

     

Notice, the integration was done with time, t, and not 5 seconds. Since the velocity at 5 seconds is not requested, only the general velocity function is determined.

Next, find the distance traveled in 5 seconds by integrating the velocity function that was just determined,

     

The final position after 5 seconds is

x = (625 + 125) / 6 = 125 m

     
Example Problem 1
   

     
Example Problem 2
   

     
Example Problem 3
   

     
Example Problem 4
   

     
Example Problem 5
   

     
Example Problem 6
   

     
Example Problem 7
   

     
Example Problem 8
   

     
Example Problem 9
   

     
Example Problem 10
   

     
Example Problem 11
   

     
Example Problem 12
   

     
Example Problem 13
   

     
Example Problem 14
   

     
Example Problem 15
   

     
Example Problem 16
   

     
Example Problem 17