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?


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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