Kinematics Lecture Notes

Introduction to Kinematics

• Kinematics describes how objects move without reference to force.
• Focus is on one-dimensional kinematics along the x-axis, sometimes y-axis.
• Two-dimensional kinematics projects topics like projectile motion.

Scalar vs Vector Quantities

• Scalar Quantity: Magnitude only (e.g., mass, distance, temperature).
• Vector Quantity: Magnitude and direction (e.g., displacement, velocity, acceleration).

Examples

• Mass: Scalar (e.g., 2kg)
• Distance vs Displacement:
  • Distance: Scalar (e.g., 15 meters)
  • Displacement: Vector (e.g., 15 meters east)
• Speed vs Velocity:
  • Speed: Scalar (e.g., 20 m/s)
  • Velocity: Vector (e.g., 30 m/s north)
• Temperature: Scalar (e.g., 80°F)
• Acceleration: Vector (e.g., 2 m/s² east)

Distance vs Displacement

• Distance: Total path length, scalar, always positive.
• Displacement: Change in position, vector, can be positive or negative.
• Example: A person travels 13 meters east and 4 meters west ->
  • Distance = 17 meters
  • Displacement = Positive 9 meters (13m east - 4m west)

Speed vs Velocity

• Speed: Rate of motion (scalar), always positive.
• Velocity: Speed with direction (vector), can be positive or negative.

Calculations

• Average Speed = Total Distance / Time
• Average Velocity = Displacement / Time

Example Problem

• A particle travels 100 meters east, then 150 meters west in 5 seconds:
  • Average Speed = 50 m/s (Total Distance = 250m)
  • Average Velocity = -10 m/s (Displacement = -50m)

Instantaneous vs Average Measurements

• Instantaneous Speed: Absolute value of instantaneous velocity.
• Instantaneous Velocity: Velocity at a specific instant.
• Average Velocity: Displacement over a time interval.

Formulas for Kinematics

Constant Speed

• Distance (d) = Speed (v) × Time (t)
• For constant speed, instantaneous velocity = average velocity.

Constant Acceleration

• Displacement (d) = ( \frac{1}{2} (V_{initial} + V_{final}) \times t )
• Final position = Initial position + Average velocity × t
• Average acceleration = Change in velocity / Time
• Final velocity = Initial velocity + Acceleration × Time
• ( V_{final}^2 = V_{initial}^2 + 2 , a , d )
• Displacement = ( V_{initial} , t + \frac{1}{2} , a , t^2 )

Example Problem: Constant Speed

• Problem: Bus travels at 40 m/s. How long to cover 200 miles?
• Convert speed to miles per hour: 40 m/s = 89.5 mph
• Time (t) = Distance (200 miles) / Speed (89.5 mph) = 2.23 hours

Example Problem: Average Velocity

• Problem: Bus moves from 50 miles east to 90 miles west of city XYZ in 5 hours.
• Initial position = 50 miles; Final position = -90 miles
• Average velocity = Displacement / Time = -28 mph

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• Note: Ensure unit consistency when performing calculations.
• Review these equations and examples to develop a stronger understanding of kinematics concepts.