A maintenance vehicle is modelled as moving on a straight tunnel track with velocity v=(t2+at+b) m s−1v=(t^2+at+b)\text{ m s}^{-1}v=(t2+at+b) m s−1. It changes direction at t=2t=2t=2 and t=6t=6t=6. Its displacement from its starting point at t=4t=4t=4 is 163\dfrac{16}{3}316 m.
Find a a\,a and bbb.
Verify the stated displacement at t=4t=4t=4.
Find the total distance travelled in the first 8 s.