1: A particle's position in the plane seconds after it starts moving is:

x=6cos(kt) , y=6sin(kt)

for some constant k . If the particle moves a distance of 120π every second, then what is k ?

The distance the particle moves is the circumference of a circle with radius 6. The circumference of a circle is 2πr, so we can set 6⋅2π=120π to get k=6.