A particle is moving

Question

A particle is moving on the perimeter of a circle with radius r = 10 with angular speed of pi/3 radians per second. After completing 3 full rotations, the particle traveled for 2 more seconds and stopped. What is the length of the total distance the particle traveled

Answer 1

There are 2 parts to this problem:

1) 3 full rotations means the particle traveled 3*C = 3(2*pi*r) = 3*2*pi*10 = 60*pi = 188.5 units

2) velocity = rw where w = the angular velocity , then v = (10)(pi/3) = 10.472 units/sec

So, in 2 seconds 10.472 units/sec x 2 sec = 20.94 units

So, in total, the particle traveled 188.5 + 20.94 units = 209.44 units