The position of an object moving along an x axis is given by x = 3.09-4.24 t² + 1.05 t³, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t= 4 s? (f) What is its average velocity from t=2stot=4s?

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Motion Along an x-axis

The position of an object moving along an x-axis is given by the function:

\[ x = 3.09t - 4.24t^2 + 1.05t^3 \]

Where:
- \( x \) is the position in meters (m)
- \( t \) is the time in seconds (s)

#### Problems:

1. **Determine the position of the object at the following values of \( t \):**
    - (a) \( t = 1 \text{ s} \)
    - (b) \( t = 2 \text{ s} \)
    - (c) \( t = 3 \text{ s} \)
    - (d) \( t = 4 \text{ s} \)
   
2. **Additional Questions:**
    - (e) What is the object's displacement between \( t = 0 \) s and \( t = 4 \) s?
    - (f) What is its average velocity from \( t = 2 \) s to \( t = 4 \) s?

#### Answer Form:

(a) Position at 1 second: \( x \) = [Text box for numerical input] [Dropdown menu for units]

(b) Position at 2 seconds: \( x \) = [Text box for numerical input] [Dropdown menu for units]

(c) Position at 3 seconds: \( x \) = [Text box for numerical input] [Dropdown menu for units]

(d) Position at 4 seconds: \( x \) = [Text box for numerical input] [Dropdown menu for units]

(e) Displacement between \( t = 0 \) s and \( t = 4 \) s: \( \Delta x \) = [Text box for numerical input] [Dropdown menu for units]

(f) Average velocity from \( t = 2 \) s to \( t = 4 \) s: \( \bar{v} \) = [Text box for numerical input] [Dropdown menu for units]

**Note:**
For (a), (b), (c), and (d), calculate the position by substituting the corresponding value of \( t \) into the equation given. For (e), find the difference in position \( x \) at \( t = 4 \) s and \( x \) at \( t = 0 \
Transcribed Image Text:### Motion Along an x-axis The position of an object moving along an x-axis is given by the function: \[ x = 3.09t - 4.24t^2 + 1.05t^3 \] Where: - \( x \) is the position in meters (m) - \( t \) is the time in seconds (s) #### Problems: 1. **Determine the position of the object at the following values of \( t \):** - (a) \( t = 1 \text{ s} \) - (b) \( t = 2 \text{ s} \) - (c) \( t = 3 \text{ s} \) - (d) \( t = 4 \text{ s} \) 2. **Additional Questions:** - (e) What is the object's displacement between \( t = 0 \) s and \( t = 4 \) s? - (f) What is its average velocity from \( t = 2 \) s to \( t = 4 \) s? #### Answer Form: (a) Position at 1 second: \( x \) = [Text box for numerical input] [Dropdown menu for units] (b) Position at 2 seconds: \( x \) = [Text box for numerical input] [Dropdown menu for units] (c) Position at 3 seconds: \( x \) = [Text box for numerical input] [Dropdown menu for units] (d) Position at 4 seconds: \( x \) = [Text box for numerical input] [Dropdown menu for units] (e) Displacement between \( t = 0 \) s and \( t = 4 \) s: \( \Delta x \) = [Text box for numerical input] [Dropdown menu for units] (f) Average velocity from \( t = 2 \) s to \( t = 4 \) s: \( \bar{v} \) = [Text box for numerical input] [Dropdown menu for units] **Note:** For (a), (b), (c), and (d), calculate the position by substituting the corresponding value of \( t \) into the equation given. For (e), find the difference in position \( x \) at \( t = 4 \) s and \( x \) at \( t = 0 \
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