Distance determined by linear acceleration and time?

Question

Here is the Question: 

The acceleration of a race car for the first few seconds of the race can be approximated by the a(t) = A + Bt linear formula, where t is the time measured in seconds and the values of the constants A and B are: A = 23.1 m/s2 and B = -2.50 m/s3. What is the speed of the car 2.30 s after it starts from rest?

I got the speed (46.5 m/s) by integrating 23.1-2.5x from 0 to 2.3. The second part of the question is what i cant figure out...

How much distance does the car cover during this 2.3 s time period?

I have tried using d=1/2at^2 but that doesnt work....Integrating 46.5 from 0-2.3 also doesnt work. Help me out here? im looking to figure out how far the car traveled....

Incorrect answers: 
107m
53.5m

Steve · Accepted Answer

a = 23.1 - 2.50*t

v = ∫a*dt = 23.1*t - 1.25*t²;  At t = 2.30 sec, v = 46.52 m/s

x = ∫v*dt = 11.55*t² - 0.4167*t³ → x = 56.03 m

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Distance determined by linear acceleration and time?

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