A particle moves in a straight-line such that its displacement, s metres, from a fixed point O at a time t seconds, is given by

S = 2t for 0 ≤ t ≤ 4,

S = 8 + 2 ln(t – 3) for t > 4.

a. Find the initial velocity of the particle.

b. Find the velocity of the particle when

i. t = 2

ii. t = 6

c. Find the acceleration of the particle when

i. t = 2

ii. t = 6.

d. Sketch the displacement-time graph for the motion of the particle.

e. Find the distance travelled by the particle in the 8^th second.