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Find the total distance traveled?

by Kratos321
Tags: calculus, differentiation
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Oct24-11, 10:33 PM
P: 20
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!
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Oct25-11, 06:20 AM
Sci Advisor
PF Gold
P: 39,682
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.

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