PHYSICS 1D03 MIDTERM 1 NOTES
AND SUMMARY
Nicely Written & Complete Study Guide
KEY TOPICS COVERED
• 1D Kinematics: Displacement, Distance, Average & Instantaneous Velocity/Acceleration,
Graphical Relationships, Constant Acceleration Equations, Free-Fall Motion
• Vectors & Coordinate Systems: Scalars vs. Vectors, Vector Arithmetic (Triangle/
Parallelogram Systems), Component Notation, Unit Vectors
• 2D Motion & Circular Motion: Position/Velocity/Acceleration Vectors, Projectile Motion
Trajectories, Uniform and Non-Uniform Circular Motion (Radial and Tangential
Accelerations), Relative Motion Frame Transformations
• Newton's Laws of Motion: Law of Inertia, Dynamic Proportionality (F = ma), Interaction
Pairs (Action-Reaction Pairs), Free-Body Diagrams
• Applications of Forces: Mass vs. Weight, Universal Gravitation, Friction Mechanics (Static
vs. Kinetic Friction), Ropes, Tension, and Atwood Systems, Elevator Dynamics (Apparent
Weight)
1
, Lesson 1: One-Dimensional Kinematics
Foundations of 1D Motion
Kinematics is quantitatively defined as the mathematical description of motion without considering the
forces or agents that cause or modify that motion. In a one-dimensional coordinate system, motion occurs
exclusively along a single linear path. Direction is unambiguously communicated via scalar signs (positive
and negative parameters) tied directly to an established reference point or origin coordinate (0, 0).
• Position x(t): The distinct spatial location of an object with respect to the designated framework origin
point at an instantaneous time. Proper units must always be written explicitly in meters (m).
• Displacement Δx: The spatial vector representing the change in linear position over a specific duration:
Δx = xf − xi. This baseline tracking parameter is exclusively dependent on the initial and final
coordinates, regardless of the intermediate path length.
• Distance: A scalar property measuring the absolute path length explicitly traversed during an object's
trajectory.
CONCEPT EXAMPLE: DISPLACEMENT SIGN ANALYSIS
An object starts moving relative to a baseline timeline tracking system. From t = 0 to t = 30 s, it moves
steadily away from the reference source point. From t = 30 s to t = 40 s, the position remains unchanged.
From t = 40 s to t = 80 s, it turns around and tracks back toward the reference point. The net displacement
calculation treats the forward tracking segment as positive values and the return loop as negative values,
whereas the total path distance calculation scales incrementally and strictly up.
Velocity Calculations and Derivative Interpretations
Velocity describes the rate of change of position with respect to time.
• Average Velocity v : Calculated over a finite timeline gap as total displacement divided by the
avg
elapsed time:
vavg = Δx / Δt = (xf − xi) / (tf − ti)
Geometrically, this value represents the unique mathematical slope of a straight secant line connecting
two coordinates on a position-versus-time graph.
• Instantaneous Velocity v(t): Defined as the limit of average velocity as the evaluated timeline gap
approaches zero, mapping directly to the first derivative of position:
v(t) = limΔt→0 (Δx / Δt) = dx / dt
Geometrically, this is the slope of the line tangent to the position-time curve at that explicit temporal
point.
2
AND SUMMARY
Nicely Written & Complete Study Guide
KEY TOPICS COVERED
• 1D Kinematics: Displacement, Distance, Average & Instantaneous Velocity/Acceleration,
Graphical Relationships, Constant Acceleration Equations, Free-Fall Motion
• Vectors & Coordinate Systems: Scalars vs. Vectors, Vector Arithmetic (Triangle/
Parallelogram Systems), Component Notation, Unit Vectors
• 2D Motion & Circular Motion: Position/Velocity/Acceleration Vectors, Projectile Motion
Trajectories, Uniform and Non-Uniform Circular Motion (Radial and Tangential
Accelerations), Relative Motion Frame Transformations
• Newton's Laws of Motion: Law of Inertia, Dynamic Proportionality (F = ma), Interaction
Pairs (Action-Reaction Pairs), Free-Body Diagrams
• Applications of Forces: Mass vs. Weight, Universal Gravitation, Friction Mechanics (Static
vs. Kinetic Friction), Ropes, Tension, and Atwood Systems, Elevator Dynamics (Apparent
Weight)
1
, Lesson 1: One-Dimensional Kinematics
Foundations of 1D Motion
Kinematics is quantitatively defined as the mathematical description of motion without considering the
forces or agents that cause or modify that motion. In a one-dimensional coordinate system, motion occurs
exclusively along a single linear path. Direction is unambiguously communicated via scalar signs (positive
and negative parameters) tied directly to an established reference point or origin coordinate (0, 0).
• Position x(t): The distinct spatial location of an object with respect to the designated framework origin
point at an instantaneous time. Proper units must always be written explicitly in meters (m).
• Displacement Δx: The spatial vector representing the change in linear position over a specific duration:
Δx = xf − xi. This baseline tracking parameter is exclusively dependent on the initial and final
coordinates, regardless of the intermediate path length.
• Distance: A scalar property measuring the absolute path length explicitly traversed during an object's
trajectory.
CONCEPT EXAMPLE: DISPLACEMENT SIGN ANALYSIS
An object starts moving relative to a baseline timeline tracking system. From t = 0 to t = 30 s, it moves
steadily away from the reference source point. From t = 30 s to t = 40 s, the position remains unchanged.
From t = 40 s to t = 80 s, it turns around and tracks back toward the reference point. The net displacement
calculation treats the forward tracking segment as positive values and the return loop as negative values,
whereas the total path distance calculation scales incrementally and strictly up.
Velocity Calculations and Derivative Interpretations
Velocity describes the rate of change of position with respect to time.
• Average Velocity v : Calculated over a finite timeline gap as total displacement divided by the
avg
elapsed time:
vavg = Δx / Δt = (xf − xi) / (tf − ti)
Geometrically, this value represents the unique mathematical slope of a straight secant line connecting
two coordinates on a position-versus-time graph.
• Instantaneous Velocity v(t): Defined as the limit of average velocity as the evaluated timeline gap
approaches zero, mapping directly to the first derivative of position:
v(t) = limΔt→0 (Δx / Δt) = dx / dt
Geometrically, this is the slope of the line tangent to the position-time curve at that explicit temporal
point.
2
