Find the total distance traveled?

In summary, to find the total distance traveled by an object moving along the x-axis at a position given by x(t) = 2 + (3/pi) - (3/pi)(cos(pi/3)t) over the time interval 0≤t≤4.5, first take the derivative to determine the speed, v. Then, calculate when v=0 to determine the intervals where the direction of motion changes. Finally, calculate the distance moved during each interval and add the absolute values to find the total distance traveled.
  • #1
Kratos321
20
0
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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  • #2
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.
 

FAQ: Find the total distance traveled?

1. How do you calculate total distance traveled?

To calculate the total distance traveled, you need to add up all the individual distances traveled. This can be done by using a formula that takes into account the speed and time for each segment of the journey.

2. What is the difference between total distance traveled and displacement?

Total distance traveled refers to the sum of all the distances covered during a journey, while displacement refers to the straight line distance between the starting and ending points of the journey.

3. How does one account for changes in direction when calculating total distance traveled?

When calculating total distance traveled, changes in direction can be accounted for by using the Pythagorean theorem to calculate the hypotenuse of a right triangle formed by the distances traveled in each direction.

4. What are some common units of measurement for total distance traveled?

The most common units of measurement for total distance traveled are kilometers, miles, and meters. Other units such as feet, yards, and nautical miles may also be used in specific contexts.

5. Can total distance traveled be negative?

No, total distance traveled cannot be negative. Distance is a measure of length and cannot have a negative value. However, displacement can be negative if the starting and ending points are in opposite directions from a reference point.

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