Find the total distance traveled?

[Kratos321]

An object moves along the x – axis and the position of the object at is given by

x(t) = 2 + (3/pi) - (3/pi)(cos(pi/3)t)

How do I find the total distance traveled by the object over the time interval 0≤t≤4.5

any help pls? I don't even know where to start. PLEASE!

 

[HallsofIvy]

First take the derivative to determine the speed, v. When is v 0? Those are the only times the direction of motion. changes You can then determine the distance movied during each interval by calculating x for those times when v=0 and subtracting x values for consecutive values of t. Of course, some of those will be negative. Add the absolute values to find the total distance moved.