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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

     
   
 
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