Overview
This lecture focused on nonuniform motion, acceleration, and graphical analysis of motion, including interpreting and drawing displacement-time, velocity-time, and acceleration-time graphs.
Uniform vs. Nonuniform Motion
- Uniform motion: object moves at constant velocity (same speed and direction).
- Nonuniform motion: object’s velocity changes (speed, direction, or both).
- Acceleration is the rate at which velocity changes with time.
Acceleration Concepts
- Acceleration occurs when an object speeds up, slows down, or changes direction.
- Acceleration is a vector (has magnitude and direction).
- Measured in m/s² (meters per second squared).
- Deceleration is acceleration in the direction opposite to velocity.
Calculating Acceleration
- Acceleration = (final velocity - initial velocity) / time.
- Positive acceleration increases speed in the positive direction; negative acceleration slows an object or increases speed in the negative direction.
- Example: If an object starts at 2 m/s and accelerates at -1 m/s², its velocity decreases by 1 m/s each second.
Graphical Analysis of Motion
- Displacement-time (d-t) graph: slope represents velocity.
- Constant slope = constant velocity (uniform motion).
- Changing slope = changing velocity (accelerated motion).
- Velocity-time (v-t) graph: slope represents acceleration.
- Area under v-t graph represents displacement.
- Read velocity directly from y-value of a v-t graph; acceleration from the slope.
Instantaneous Velocity
- Instantaneous velocity: the velocity at a specific instant during nonuniform motion.
- Found by calculating the slope of the tangent to a point on a d-t graph.
Graph Relationships & Interpretation
- On a d-t graph, a steeper slope means higher velocity.
- On a v-t graph, a new slope or change in sign indicates acceleration or deceleration.
- Area under v-t graphs (using geometric shapes) provides displacement.
- Acceleration-time (a-t) graphs: constant values for uniform acceleration; zero for uniform velocity.
Key Terms & Definitions
- Uniform Motion — Motion at a constant velocity.
- Nonuniform Motion — Motion with changing velocity (accelerated motion).
- Velocity — Speed in a specified direction (vector).
- Acceleration — Rate of change of velocity, measured in m/s².
- Deceleration — Acceleration opposite to the direction of velocity.
- Displacement-Time Graph (d-t) — Graph showing position over time; slope is velocity.
- Velocity-Time Graph (v-t) — Graph showing velocity over time; slope is acceleration, area is displacement.
- Instantaneous Velocity — Velocity at a particular moment; the slope of the tangent to a d-t graph at that point.
- Tangent Line — A straight line that touches a curve at one point and represents the slope at that point.
Action Items / Next Steps
- Complete page 27, number 2 from your assignment.
- Finish the remaining practice problems for this lesson.
- Review graphical analysis steps and practice drawing and interpreting d-t, v-t, and a-t graphs.
- Reach out for help if clarification is needed.