Overview
This lecture introduces the basics of kinematics in classical mechanics, focusing on key equations describing horizontal motion without involving forces.
Mechanics and Kinematics
- Mechanics is the branch of physics dealing with motion, divided into kinematics and dynamics.
- Kinematics studies motion using equations without considering forces.
- Dynamics examines how forces affect motion.
Kinematic Equations
- Kinematic equations describe motion in one and two dimensions using displacement, velocity, acceleration, and time.
- In basic kinematics, acceleration is treated as constant.
Fundamental Kinematic Equations
- ( v = v_0 + at ): Final velocity equals initial velocity plus acceleration times time.
- ( x = x_0 + v_0 t + \frac{1}{2} a t^2 ): Position equals initial position plus initial velocity times time plus half the acceleration times time squared.
- ( v^2 = v_0^2 + 2a(x - x_0) ): Final velocity squared equals initial velocity squared plus two times acceleration times displacement.
Supplemental Equations
- ( x = v_{avg} \Delta t ): Position equals average velocity times time interval.
- ( v_{avg} = \frac{v + v_0}{2} ): Average velocity is the mean of initial and final velocity.
Example Problems
- For a car accelerating at 2.5 m/sĀ² from rest for 10 seconds: final velocity is 25 m/s, distance is 125 meters.
- For a car decelerating from 27 m/s at -8.4 m/sĀ²: time to stop is 3.2 seconds, stopping distance is 43 meters.
Key Terms & Definitions
- Kinematics ā Study of motion without regard to forces.
- Dynamics ā Study of how forces affect the motion of objects.
- Displacement ((x)) ā Change in position.
- Velocity ((v)) ā Rate of change of displacement.
- Acceleration ((a)) ā Rate of change of velocity.
- Initial value (subscript 0) ā Value of a variable at the start (e.g., (v_0) is initial velocity).
Action Items / Next Steps
- Practice solving problems using the kinematic equations for various scenarios.
- Review definitions of displacement, velocity, and acceleration.