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