Overview
This lecture introduces the basics of motion in physics, focusing on the concepts of time, position, velocity, acceleration, and the use of kinematic equations for analyzing one-dimensional motion.
The Science of Motion
- Physics studies how things move, using concepts like time, position, velocity, and acceleration.
- Motion in a straight line is called one-dimensional motion.
- Direction in one-dimensional motion is arbitrary but must be consistent throughout calculations.
Key Conditions of Motion
- Time tells you how long an event occurs.
- Position describes where you are; can be positive or negative depending on chosen direction.
- Displacement is the change in position and can be positive or negative.
- Velocity is the rate of change of position over time and includes direction.
- Acceleration is the rate at which velocity changes over time.
Graphing Motion
- Position vs. time graphs show how position changes as time passes (position on y-axis, time on x-axis).
- A flat line on a position-time graph means no movement; a diagonal line means constant velocity; a curved line means acceleration.
- Velocity vs. time graphs and acceleration vs. time graphs similarly help visualize changes in motion.
Core Equations of Motion
- Average velocity: ( \bar{v} = \Delta x / \Delta t ) (change in position over change in time).
- Average acceleration: ( a = \Delta v / \Delta t ) (change in velocity over change in time).
- Definition of acceleration (first kinematic equation): ( v = v_0 + at ).
- Displacement curve (second kinematic equation): relates acceleration, starting velocity, time, and displacement.
- Other kinematic equations are algebraic rearrangements of these two main equations.
Applying Kinematic Equations
- Use known values (initial velocity, time, acceleration) to solve for unknowns (final velocity, displacement).
- Example: Using the displacement curve and definition of acceleration to determine final speed in a speeding scenario.
Key Terms & Definitions
- Displacement — change in position (( \Delta x )), can be negative or positive.
- Velocity (( v )) — rate of change of position with direction, measured in meters per second (m/s).
- Acceleration (( a )) — rate of change of velocity, measured in meters per second squared (m/s²).
- Kinematic equations — formulas relating time, position, velocity, and acceleration for motion with constant acceleration.
- g — acceleration due to gravity, ( 9.81, m/s^2 ).
Action Items / Next Steps
- Review and memorize the two main kinematic equations.
- Practice sketching and interpreting position vs. time, velocity vs. time, and acceleration vs. time graphs.
- Try solving sample problems using the kinematic equations for various initial conditions.