A particle moves along a straight line with its position at time ( t ) given by the equation \( s(t) = 3t3 – 12t2 + 9t + 5 \), where( s(t) ) is the position in meters and \

( t ) is the time in seconds.

(a)Determine the velocity of the particle at any time ( t ). (5 marks)

(b) Find the acceleration of the particle at any time ( t ). (5 marks)

(c)At what time(s) is the particle at rest? (5 marks)

(d) Determine the total distance traveled by the particle during the first 4 seconds. (5 marks)