A particle P P\,P moves on the x x\,x axis. The acceleration of P P\,P at time t t\,t seconds is (6t−24) m s−2(6t - 24) \text{ m s}^{-2}(6t−24) m s−2 measured in the positive x x\,x direction. Initially the particle is at O O\,O with a velocity of 60 m s-1.
Show that the particle will never travel in the negative x x\,x direction.
Find the distance travelled by the particle in the first 10 seconds.