A particle moves along the xxx-axis. Its acceleration at time t t\,t seconds is (6t−8) m s−2(6t-8)\text{ m s}^{-2}(6t−8) m s−2. Its initial velocity is 7 m s-1 and its initial displacement is zero.
Show that the particle never moves in the negative xxx-direction.
Find the distance travelled in the first 5 seconds.