Lecture 1 1d Kinematics

One-Dimensional Kinematics

Overview

• Kinematics studies motion without considering the forces behind it.

• Focus on basic concepts: position, velocity, and acceleration.

• Introduces calculus concepts such as differentiation and integration.

• Examines motion of a particle along a line, using a reference point (origin O).

Position

• Defined as the distance from the origin (O):

  • Positive if to the right of O.

  • Negative if to the left of O.

• Units of Measurement:

  • Measured in units of length (e.g., feet, meters, light-years).

  • Standard unit: meters (S.I. units).

Motion and Position/Time Graphs

• Position (s) changes with time (t).

• Notation: s(t) indicates position is a function of time.

• Units of Time:

  • Measured in seconds (preferred), or other units such as years or minutes.

• Graphing Motion:

  • Plot time (t) on the horizontal axis and position (s) on the vertical axis.

  • Visualizing motion:

    • (a) s constant → particle at rest.

    • (b) s steadily increases → particle moving forward.

    • (c) particle moves out then returns to the origin.

    • (d) particle oscillates back and forth through the origin.

Velocity

• Velocity measures the rate of change of position (s) over time (t).

• Quantifies how quickly the position changes and in which direction.

  • Example (a): If s is constant, velocity = 0 (particle at rest).

  • Example (b): For a linear s vs. t graph:

    • Change in position: s2 - s1.

    • Change in time: t2 - t1.

• Velocity Definition:

  • v = (s2 - s1) / (t2 - t1)

  • Slope of the s vs. t graph indicates velocity (tan ϕ).

Units of Velocity

• If s is in meters and t in seconds, then:

  • Velocity v = meters per second (m/s).

• Velocity sign indicates direction:

  • v > 0: Positive slope → moving right.

  • v < 0: Negative slope → moving left.