Big Five Kinematics, Uniform Acceleration, How to Select, Intervals, Objects - Physics (Mechanics)

The "big five" in kinematics refers to the five key quantities used to describe motion with constant acceleration: displacement (\(\Delta x\)), initial velocity (\(v_{i}\)), final velocity (\(v_{f}\)), acceleration (\(a\)), and time (\(t\)). These five quantities are interconnected by five fundamental kinematic equations, allowing you to solve for an unknown variable if you know the other four.

💡The five kinematic quantities
• Displacement (\(\Delta x\) or \(s\)): The change in an object's position, measured in meters (m).
• Initial velocity (\(v_{i}\) or \(u\)): The velocity of an object at the beginning of a time interval, measured in meters per second (m/s).
• Final velocity (\(v_{f}\) or \(v\)): The velocity of an object at the end of a time interval, measured in meters per second (m/s).
• Acceleration (\(a\)): The rate at which velocity changes, measured in meters per second squared (\(m/s^{2}\)).
• Time (\(t\)): The duration of the motion, measured in seconds (s).

💡The five kinematic equations
These equations apply when acceleration is constant.
• \(v_{f}=v_{i}+at\)
• \(\Delta x=v_{i}t+\frac{1}{2}at^{2}\)
• \(v_{f}^{2}=v_{i}^{2}+2a\Delta x\)
• \(\Delta x=\frac{1}{2}(v_{i}+v_{f})t\)
• \(v_{avg}=\frac{v_{i}+v_{f}}{2}\) and \(\Delta x=v_{avg}t\) (when acceleration is constant, average velocity is the arithmetic mean of the initial and final velocities)

💡How to use the big five
• Identify the known and unknown variables in a given problem.
• Select the equation that contains the known variables and the one you want to find.
• Solve the equation for the unknown variable.

💡Worksheets are provided in PDF format to further improve your understanding:
• Questions Worksheet: https://drive.google.com/file/d/1FZHK2lvewIfauVNmVxQprxLvhBZfVv02/view?usp=drive_link
• Answers: https://drive.google.com/file/d/1h8pFAHvhQo5qqSPsfYA9GETrdjMQg8z8/view?usp=drive_link

💡Chapters:
00:00 Big five kinematic equations
02:26 Selecting kinematic equations, multiple intervals
04:34 Selecting kinematic equations, multiple objects
06:02 Worked examples

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