(i) Velocity is the rate of change of distance ds/dt:
ds/dt=6t²-8t+2 m/s
(ii) Acceleration is rate of change of velocity, d²s/dt²=12t-8, which is 24-8=16m/s² when t=2.
(iii) Particle is at rest when velocity=0, so 6t²-8t+2=0=3t²-4t+1=(3t-1)(t-1), so t=⅓ and 1 second when the particle is at rest. Distance for these times is s(⅓)=2/27-4/9+2/3=(2-12+18)/27=8/27 m; and s(1)=2-4+2=0. So the particle is at rest at distances of 8/27 m and 0 m.