Overview
This lecture covers the fundamental concepts and calculations involving distance, speed, and time, including how to use the distance-speed-time triangle and convert between units.
Core Concepts: Distance, Speed, and Time
- Distance measures how far one point is from another (e.g., meters, kilometers).
- Speed measures how fast movement occurs and is calculated as distance divided by time.
- Time measures the duration taken to travel between two points (e.g., seconds, minutes, hours).
The Distance-Speed-Time Triangle
- Use the triangle to determine which formula to use: distance (D) at the top, speed (S) and time (T) at the bottom.
- To find distance: D = S × T.
- To find speed: S = D ÷ T.
- To find time: T = D ÷ S.
- Cover the unit you need to find, then multiply if the others are next to each other or divide if one is above the other.
Units and Conversions
- The unit for speed depends on units for distance and time (e.g., km/h, m/s).
- To convert meters to kilometers, divide by 1000.
- To convert minutes to hours, divide by 60.
- To convert hours (with decimals) to hours and minutes, multiply the decimal by 60 for minutes.
Example Problems
- Example 1: Find time if distance is 130 km and speed is 120 km/h; T = 130 ÷ 120 = 1.0833 hours (1 hour, 5 minutes).
- Example 2: Find speed if distance is 1.2 million meters and time is 13 hours 20 minutes; convert distance to km and time to hours, then S = D ÷ T.
- Example 3: Given distance, speed, and arrival time, determine departure time by calculating total travel time and subtracting from arrival.
Problem Solving Tips
- Always check that units for distance and time match the required speed units.
- Be careful when converting between hours, minutes, and decimals.
- Read questions thoroughly to apply the correct formula and conversion.
Key Terms & Definitions
- Distance — How far two points are from each other (e.g., meters, kilometers).
- Speed — The rate of movement; calculated as distance divided by time (e.g., km/h, m/s).
- Time — The duration of motion from start to end (e.g., seconds, minutes, hours).
Action Items / Next Steps
- Practice problems converting between hours, minutes, and decimals.
- Review any referenced video on measurement conversions as needed.
- Be sure to memorize the distance-speed-time triangle for solving related problems.