Question
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The figure shows the velocity function for motion along a line.
Assume the motion begins with an initial position of .
Determine the following.
a. The displacement between and .
b. The distance traveled between and .
c. The position at .
a. The displacement is unit(s).
(Simplify your answer. Type an integer or a fraction.)
b. The distance traveled between and is unit(s).
(Simplify your answer. Type an integer or a fraction.)
c. The position at is .
(Simplify your answer. Type an integer or a fraction.)

Ask by Powers Byrd. in the United States
Jan 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The position at is units.

Solution

c. The position at is .
Explanation:
  • Displacement ( ) is the net change in position from to , which is given as units.
  • Position at can be found using the relation:
    Given that the initial position :
Final Answer:

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Bonus Knowledge

If we assume that the velocity function is given graphically and you’re looking for position and distance traveled, you can find the answers with some careful calculations.
To find the position at , use the formula for displacement, which was already found as . Since you started from an initial position of , simply add the displacement to it:
Now, you need to compute the distance traveled. Since the distance involves the total movement regardless of direction, you’ll consider the absolute values of displacement over the interval. You already noted that the distance traveled is units. Therefore, to wrap it all up:
c. The position at is units.

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