Overview
This lecture introduces kinematics, focusing on equations that describe the motion of objects in one dimension, with practical examples for horizontal motion.
Mechanics and Kinematics
- Mechanics is a branch of physics divided into kinematics (motion without forces) and dynamics (effect of forces on motion).
- Kinematics, developed by Galileo, studies equations for motion without considering forces.
- Final kinematics equations apply broadly, but real-world variables (e.g., friction) may require simplifications.
Kinematic Equations and Variables
- Kinematic equations relate displacement, velocity, acceleration (constant), and time.
- A subscript zero (e.g., vā or xā) indicates the initial value of a variable.
- Key variables: displacement (x), initial displacement (xā), velocity (v), initial velocity (vā), acceleration (a), and time (t).
Fundamental Kinematic Equations
- ( v = v_0 + a t ) (velocity after time t)
- ( x = x_0 + v_0 t + \frac{1}{2} a t^2 ) (position after time t)
- ( v^2 = v_0^2 + 2 a (x - x_0) ) (velocity-displacement relationship)
- Supplemental: ( x = v_{avg} \Delta t ) and ( v_{avg} = \frac{v + v_0}{2} )
Example Problems
- Starting from rest with ( a = 2.5, m/s^2 ) for 10 seconds:
- Final velocity: ( v = 25, m/s )
- Distance traveled: ( x = 125, m )
- Decelerating from ( v_0 = 27, m/s ), ( a = -8.4, m/s^2 ):
- Time to stop: ( t = 3.2, s )
- Stopping distance: ( x = 43, m )
Key Terms & Definitions
- Mechanics ā the study of motion and forces.
- Kinematics ā study of motion without regard to causes (forces).
- Dynamics ā study of the effect of forces on motion.
- Displacement (x) ā change in position.
- Velocity (v) ā rate of change of displacement.
- Acceleration (a) ā rate of change of velocity (assumed constant in kinematics).
- Initial (subscript 0) ā value at the start of observation.
Action Items / Next Steps
- Practice applying kinematic equations to solve for unknowns.
- Prepare for next tutorial by reviewing examples of one-dimensional motion.