A tracking carriage moves along a straight rail with acceleration a=(6t−12) m s−2a=(6t-12)\text{ m s}^{-2}a=(6t−12) m s−2. At t=0t=0t=0 it is at the origin and has velocity u m s−1u\text{ m s}^{-1}u m s−1. The carriage returns to the origin at t=4t=4t=4 s.
Find uuu.
Find the total distance travelled by the carriage in the first 4 s. Give your answer in exact form.