- [Maximum mark: 8]
A particle starts from rest at point O and moves in a straight line with velocity, v, given by
v = 3 sin(t)(1 + cos(t)), t ≥ 0
where v is measured in metres per second and time, t (radians), is measured in seconds.
The particle next comes to instantaneous rest when t = a.
(a) Determine the value of a. [2]
(b) Find the maximum velocity of the particle during the interval 0 ≤ t ≤ a. [2]
(c) By finding the total distance travelled between t = 0 and t = a, find the average speed of the particle during the interval 0 ≤ t ≤ a. [4]