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?
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
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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 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643aff56-d3d2-46ec-80fe-61025699ffb7%2F34112631-f9c1-4f7e-8529-63cbc98cc99e%2Fw3lz7v_processed.jpeg&w=3840&q=75)
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