Graphs of Motion

Study Notes

Graphs Of Motion

Position-Time Graphs:
- Slope represents velocity.
- Steeper slope indicates higher velocity.
- Horizontal line indicates no motion.
Velocity-Time Graphs:
- Slope represents acceleration.
- Area under the curve indicates displacement.
- A horizontal line shows constant velocity.
Acceleration-Time Graphs:
- Area under the curve indicates change in velocity.
- Constant acceleration is represented by a horizontal line.

Acceleration

Definition: Change of velocity per unit time.
Formula: ( a = \frac{\Delta v}{\Delta t} )
Types:
- Positive Acceleration: Velocity increases.
- Negative Acceleration (Deceleration): Velocity decreases.
Unit: m/s².

Speed Vs Velocity

Speed:
- Scalar quantity.
- Measures how fast an object moves; does not include direction.
- Average speed: Total distance / Total time.
Velocity:
- Vector quantity.
- Measures speed in a specified direction.
- Average velocity: Displacement / Total time.

Displacement Vs Distance

Distance:
- Scalar quantity.
- Total path length traveled by an object.
- Always positive, depends on the path taken.
Displacement:
- Vector quantity.
- Shortest path from initial to final position.
- Can be positive, negative, or zero depending on the direction.

Equations Of Motion

Uniform Acceleration Equations (for linear motion):
1. ( v = u + at )
  - ( v ): final velocity, ( u ): initial velocity, ( a ): acceleration, ( t ): time.
2. ( s = ut + \frac{1}{2}at^2 )
  - ( s ): displacement.
3. ( v^2 = u^2 + 2as )
  - Relates velocity, acceleration, and displacement without time.
Assumptions:
- Motion is in a straight line.
- Acceleration is constant.

Graphs of Motion

Position-Time Graphs depict an object's position relative to time.
The slope indicates velocity; steeper slopes reflect higher velocities.
A horizontal line signifies that the object is at rest (no motion).
Velocity-Time Graphs show how velocity changes over time.
The slope of these graphs indicates acceleration; a flat line indicates constant velocity.
The area under the curve represents the total displacement during the time interval.
Acceleration-Time Graphs represent how acceleration varies over time.
The area under these graphs indicates the change in velocity.
Constant acceleration is depicted as a horizontal line on this graph.

Acceleration

Defined as the rate of change of velocity with respect to time.
The formula for acceleration is ( a = \frac{\Delta v}{\Delta t} ).
Positive acceleration occurs when an object's velocity increases.
Negative acceleration, or deceleration, happens when an object's velocity decreases.
Acceleration is measured in meters per second squared (m/s²).

Speed vs Velocity

Speed is a scalar quantity, quantifying how fast an object is moving without accounting for direction.
Average speed is calculated by dividing total distance traveled by total time taken.
Velocity is a vector quantity, including both speed and direction of an object's movement.
Average velocity is determined by dividing displacement by total time.

Displacement vs Distance

Distance is a scalar quantity that measures the total path length traveled by an object.
It is always a positive value and depends on the actual path taken.
Displacement is a vector quantity representing the shortest path from an object's initial to final position.
Displacement can be positive, negative, or zero based on direction relative to a reference point.

Equations of Motion

The three primary equations describe motion under uniform acceleration in linear paths:
- ( v = u + at ) relates final velocity (v), initial velocity (u), acceleration (a), and time (t).
- ( s = ut + \frac{1}{2}at^2 ) represents displacement (s) over time considering initial velocity and acceleration.
- ( v^2 = u^2 + 2as ) connects velocity, acceleration, and displacement without involving time.
Assumptions for these equations include straight-line motion and constant acceleration throughout the interval.

Description

This quiz explores the essential concepts of position-time, velocity-time, and acceleration-time graphs. Understand how the slope represents key factors like velocity and acceleration, and gain insights into their graphical representations. Perfect for physics students looking to deepen their knowledge of motion graphs.