Overview
This lecture covers the basic concepts of position, velocity, and acceleration versus time for a particle, differences between distance and displacement, and fundamentals of graphical analysis in kinematics.
Dynamics and Particle Assumptions
- A particle in dynamics is an object with mass but negligible size and shape (point mass).
- Particles only have translational motion, not rotational motion.
- Statics deals with systems at equilibrium (sum of forces is zero).
- Dynamics involves moving objects, so the sum of forces equals mass times acceleration (Newton’s Second Law).
- Dynamics splits into kinematics (study of motion) and kinetics (study of forces causing motion).
Position, Distance, and Displacement
- Position (s) is the location of a particle along a straight path from a reference origin.
- Displacement (Δs) is the change in position: final position minus initial position.
- Total distance traveled (sₜ) can be greater than displacement if the particle changes direction.
Velocity and Speed
- Average velocity (v_avg) is displacement divided by time interval: v_avg = Δs / Δt.
- Average speed is total distance traveled divided by time: avg speed = sₜ / Δt.
- Instantaneous velocity (v) is the derivative of position with respect to time: v = ds/dt.
Acceleration
- Average acceleration (a_avg) is the change in velocity over time: a_avg = Δv / Δt.
- Instantaneous acceleration (a) is the derivative of velocity with respect to time: a = dv/dt or d²s/dt².
- Acceleration in the direction of velocity speeds up the particle ("acceleration").
- Acceleration opposite to velocity slows the particle down ("deceleration").
Key Terms & Definitions
- Particle — An object with mass but negligible size and shape, treated as a point.
- Displacement (Δs) — Change in position; final position minus initial position.
- Distance (sₜ) — Total path length traveled by the particle.
- Velocity (v) — Rate of change of position with time; ds/dt.
- Speed — Magnitude of velocity; total distance over time.
- Acceleration (a) — Rate of change of velocity with time; dv/dt or d²s/dt².
- Deceleration — Acceleration in the direction opposite to velocity, causing a slowdown.
Action Items / Next Steps
- Review the summary and example in the next lecture video.