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