5. A particle moves in a straight line such that it's position relative to some origin O, is given by s(t)=(2k/t+1)+2t cm, where t is the time in seconds and k is a real constant. If the initial position of the particle is 8 cm to the right of O, show that k = 4. (1) Find expressions for the particle's velocity and acceleration.
(ii) When does the particle changes its direction of motion?
(iii) Show that the velocity of the particle is always increasing,
(iv) Sketch the graphs of v(t) and a(t) against 1, showing all the important features of the 1 curves. Hence, find the time interval(s) when the particle is increasing in speed,
(v) Draw a motion diagram for the particle for t>0.
(vi) Find the total distance travelled by the particle in the first second of motion.
[20 marks]