Kinematics Overview

Overview

This lecture introduces 1D kinematics, focusing on how to describe motion using scalar and vector quantities, and provides key formulas for solving problems involving constant speed and acceleration.

Scalars vs. Vectors

• Scalar quantities have only magnitude (e.g., mass, distance, speed, temperature).
• Vector quantities have both magnitude and direction (e.g., displacement, velocity, acceleration).
• Mass and temperature are scalars; displacement, velocity, and acceleration are vectors.
• Distance is scalar (total length traveled); displacement is vector (net change in position with direction).

Distance, Displacement, Speed, and Velocity

• Displacement = final position − initial position; can be positive or negative.
• Distance is always positive and is the sum of all path segments.
• Speed = distance / time; always positive and scalar.
• Velocity = displacement / time; can be negative or positive and is vector.

Example Calculations

• For 100 m east and 150 m west in 5 s: total distance = 250 m, average speed = 50 m/s.
• Displacement = −50 m, average velocity = −10 m/s.

Formulas for Constant Speed and Acceleration

• For constant speed: ( d = vt ) (d: distance/displacement, v: speed/velocity, t: time).
• For constant acceleration:
  • ( d = \bar{v} t ), where ( \bar{v} = (v_{initial} + v_{final})/2 )
  • ( d = v_{initial} t + \frac{1}{2} a t^2 )
  • ( v_{final} = v_{initial} + at )
  • ( v_{final}^2 = v_{initial}^2 + 2ad )
  • ( x_{final} = x_{initial} + \bar{v} t )

Unit Conversions and Problem Solving

• Always match units (e.g., convert m/s to mi/h when needed).
• To convert 40 m/s to mi/h: ( 40 \times \frac{1}{1000} \times \frac{1}{1.609} \times 60 \times 60 = 89.5 ) mi/h.
• To solve for time: ( t = d/v ).
• For displacement between positions east and west of a city: displacement = final position − initial position.

Key Terms & Definitions

• Scalar — Quantity with magnitude only.
• Vector — Quantity with both magnitude and direction.
• Displacement — Change in position; vector.
• Distance — Total path length traveled; scalar.
• Speed — Distance divided by time; scalar.
• Velocity — Displacement divided by time; vector.
• Average velocity — Displacement divided by total time.
• Instantaneous velocity — Velocity at a specific instant.
• Acceleration — Change in velocity per unit time; vector.

Action Items / Next Steps

• Write down and memorize key kinematics formulas.
• Practice unit conversions for speed and distance.
• Solve example problems applying the discussed formulas.