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.
![**Question C**: What is the object's average acceleration between \( t = 0 \, \text{s} \) and \( t = 7 \, \text{s} \)?
**Question D**: When is the object's average velocity equal to zero?
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These questions aim to enhance your understanding of motion concepts in physics, particularly focusing on acceleration and average velocity.
- **Average Acceleration**: Acceleration is the rate of change of velocity. To find the average acceleration over a time interval, you can use the equation:
\[
\text{Average Acceleration} = \frac{\Delta v}{\Delta t}
\]
where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time.
- **Average Velocity**: The average velocity is the total displacement divided by the total time. It is zero when the object's displacement over a time period is zero, meaning the object returns to its starting position.
Consider using graphs or mathematical examples to solve these kinds of problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F508708ec-9232-43f6-b402-eeec6321d526%2F53c05cf7-7a6f-4892-bdb5-fcccc494fafc%2Flpzpx17_processed.jpeg&w=3840&q=75)
![## Problem Statement
**1. The position of an object as a function of time obeys the equation:**
\[
x(t) = 5t^2 - 8t + 3
\]
**Assume proper SI units.**
### Exercises
**a.** What is the object's average velocity in the x-direction between \( t=0 \, \text{s} \) and \( t=7 \, \text{s} \)?
**b.** What is the object's instantaneous velocity in the x-direction at \( t=7 \, \text{s} \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F508708ec-9232-43f6-b402-eeec6321d526%2F53c05cf7-7a6f-4892-bdb5-fcccc494fafc%2Fh1j5rg_processed.jpeg&w=3840&q=75)
The position the particle is given by
X(t) = 5t^2 - 8t + 3
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