BackKinematics: Motion, Velocity, and Acceleration (Lecture 3, Sections 2.4–2.7)
Study Guide - Smart Notes
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Kinematics in One Dimension
Position, Velocity, and Acceleration
Kinematics is the study of motion without considering its causes. In one dimension, we analyze how an object's position changes over time, and how velocity and acceleration describe this motion.
Position-versus-time graph: Plots position (x) on the vertical axis against time (t) on the horizontal axis.
Velocity: The slope of the position-versus-time graph. It represents the rate of change of position.
Uniform motion: An object moves with constant velocity; its position graph is a straight line.
Non-uniform motion: The position graph is non-linear. The slope of the tangent line at any point gives the instantaneous velocity.
Example: If an object moves 60 m in 4.0 s, its average velocity is:
Section 2.4: Acceleration
Definition and Calculation
Acceleration describes how an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction.
Acceleration: The rate of change of velocity with respect to time.
Formula:
Graphical interpretation: The slope of a velocity-versus-time graph gives the acceleration.
Units of Acceleration
The SI unit of acceleration is meters per second squared (m/s2).
Example: If a car increases its velocity from 0 to 27 m/s in 3.6 s, its acceleration is:
Acceleration is often abbreviated as "m/s2" and read as "meters per second squared."
Performance Data for Vehicles
Acceleration can be compared using vehicle performance data.
Vehicle | Time to go from 0 to 60 mph |
|---|---|
2016 Chevy Corvette | 3.6 s |
2016 Chevy Sonic | 9.0 s |
Representing Acceleration
Velocity-versus-Time Graphs
Acceleration is visually represented as the slope of the velocity-versus-time graph. For constant acceleration, this graph is a straight line.
Example Table:
Time (s) | Velocity of Sonic (m/s) | Velocity of Corvette (m/s) |
|---|---|---|
0 | 0 | 0 |
1 | 3.0 | 7.5 |
2 | 6.0 | 15.0 |
3 | 9.0 | 22.5 |
4 | 12.0 | 30.0 |
The slope (rise/run) of the velocity graph gives the acceleration.
Summary of Key Concepts
Position-versus-time graph: Slope gives velocity.
Velocity-versus-time graph: Slope gives acceleration.
Uniform motion: Constant velocity, zero acceleration.
Non-uniform motion: Changing velocity, non-zero acceleration.
Acceleration: Rate of change of velocity, measured in m/s2.
Additional info: These notes cover foundational concepts in kinematics, including graphical analysis and real-world applications such as vehicle acceleration.
