A particle is projected to the right from the position x=0 with an initial velocity of 9 m/s. If the acceleration of the particle is defined by the relation a = -0.6v³, where a and v are expressed in m/s² and m/s, respectively, determine (a) the distance the particle will have traveled when its velocity is 4 m/s, (b) the time when t = 1 m/s, (c) the time required for the particle to travel 6 m.
a) 15 m, 1.73 s, 2.45 s
b) 17 m, 1.82 s, 2.60 s
c) 20 m, 2.10 s, 2.80 s
d) 22 m, 2.24 s, 3.05 s