Question: A motorist drives along a straight road at a constant speed of 80 m/s. At t = 0 she passes a parked motorcycle police officer, and the officer takes off after her with acceleration, a(t) = bt, where b is a constant and t is the time (i.e., the acceleration varies linearly with time). If the officer maintains this rate of acceleration, what is the speed of the police officer when he reaches the motorist (in m/s)?

Please show work clearly and concisely. If you can upload a picture with the work done by hand that would be greatly appreciated. I know the answer, but don’t know how to get it, therefore the work is the only thing I care about.