Lecture on Speed, Distance, and Time

Introduction

• Focus on problems involving speed, distance, and time.
• Understanding speed as a measure of distance traveled over a period of time.

Key Concepts

1. Speed

   • Measured in units like miles per hour (mph), kilometers per hour (km/h), or meters per second (m/s).
   • Example: A car traveling at 30 mph moves 30 miles in one hour.
   • Formula: Speed = Distance / Time

2. Distance

   • Calculated by multiplying speed by time.
   • Formula: Distance = Speed × Time

3. Time

   • Determined by dividing distance by speed.
   • Formula: Time = Distance / Speed

Understanding Time Units and Conversion

• Convert time into consistent units (e.g., hours or minutes).
• Example Conversions:
  • 30 minutes = 0.5 hours
  • 15 minutes = 0.25 hours
  • 45 minutes = 0.75 hours

Problem-Solving Techniques

• Use a triangle diagram (SDT) to remember formulas:
  • Cover the variable you want to find:
    • S (Speed) = D (Distance) / T (Time)
    • D = S × T
    • T = D / S

Example Problems

1. Average Speed Calculation

   • Problem: A car travels 180 miles in 4 hours.
   • Solution: Speed = 180 miles / 4 hours = 45 mph.

2. Speed in Different Units

   • Problem: Kevin runs 400 meters in 50 seconds.
   • Solution: Speed = 400 meters / 50 seconds = 8 meters/second.

3. Time Calculation

   • Problem: A train travels 175 miles at 25 mph.
   • Solution: Time = 175 miles / 25 mph = 7 hours.

4. Distance Calculation

   • Problem: A bird flies for 6 hours at 40 km/h.
   • Solution: Distance = 40 km/h × 6 hours = 240 kilometers.

5. Handling Mixed Time Units

   • Problem: A helicopter flies 200 miles in 2 hours and 30 minutes.
   • Solution: Convert 2 hours 30 minutes to 2.5 hours.
     • Speed = 200 miles / 2.5 hours = 80 mph.

6. Complex Calculations

   • Problem: A car travels 240 km in 3 hours 40 minutes.
   • Solution: Convert 40 minutes to 0.666 hours.
     • Speed = 240 km / 3.666 hours = 65.8 km/h (rounded to two decimal places).

7. Handling Hours and Minutes for Duration

   • Problem: A journey lasts 4.2 hours.
   • Solution: Convert 0.2 hours to minutes: 0.2 × 60 = 12 minutes.
     • Total journey = 4 hours 12 minutes.

Key Takeaways

• Relationships: Speed, distance, and time are interrelated through simple formulas.
• Units and Conversion: Ensure consistency in units when solving problems.
• Problem-Solving Strategy: Use formulas, conversions, and diagrams efficiently to solve various problems in exams.