The velocity-time graph of a particle consists of straight-line segments joining the points (0,4)(0,4)(0,4), (3,10)(3,10)(3,10), (8,10)(8,10)(8,10) and (12,−6)(12,-6)(12,−6), where time is measured in seconds and velocity in metres per second.
Find the acceleration of the particle during each of the intervals 0<t<30<t<30<t<3, 3<t<8 3<t<8\,3<t<8 and 8<t<128<t<128<t<12.
Find the time at which the particle changes direction.
Determine the displacement of the particle from t=0t=0t=0 to t=12t=12t=12.
Determine the total distance travelled from t=0t=0t=0 to t=12t=12t=12.