"Rate" is a measure of how one quantity changes in relation to another—usually time. This lesson is highly practical and focuses on two key applications: Speed (the rate of change of distance) and Rate of Flow (the rate of change of volume). Mastering unit conversions is the key to success here.

Part A: Speed, Distance, and Time

1. Core Concepts (Short Notes)

• Speed: The distance an object travels in a single unit of time (e.g., per second or per hour).

• Uniform Speed: The speed remains constant throughout the journey.

• Average Speed: The overall speed for an entire journey, calculated by dividing the total distance by the total time. This is not the average of the different speeds.

2. Key Formulas

The relationship between Speed (S), Distance (D), and Time (T) is fundamental.

• Distance = Speed × Time

• Speed = Distance / Time

• Time = Distance / Speed

• Average Speed = Total Distance Travelled / Total Time Taken

3. Exam Tips & Tricks

• CRITICAL SKILL: Unit Conversion This is the most common place to lose marks. Always convert units to be consistent before you calculate.

  • km/h to m/s: Multiply by 5/18.

    • Example: 72 km/h = 72 × (5/18) = 4 × 5 = 20 m/s.

  • m/s to km/h: Multiply by 18/5.

    • Example: 15 m/s = 15 × (18/5) = 3 × 18 = 54 km/h.

• Train Problems: Always Sketch the Distance!

  • Passing a Single Point (a post, a person): The total distance the train travels to pass the point is its own length.

    • Distance = Length of Train

  • Passing a Platform or Bridge: The train must travel its own length plus the length of the platform to fully clear it.

    • Distance = Length of Train + Length of Platform

• The Average Speed Trap Never just average the speeds. You must calculate the total distance and total time for the whole journey first.

  • Problem: A car travels 15 minutes at 40 km/h, then 30 minutes at 80 km/h. Find the average speed.

  • Step 1: Find distance for each part. (Time must be in hours: 15 min = 0.25 h, 30 min = 0.5 h)

    • Part 1: D = S × T = 40 × 0.25 = 10 km

    • Part 2: D = S × T = 80 × 0.5 = 40 km

  • Step 2: Find totals.

    • Total Distance = 10 + 40 = 50 km

    • Total Time = 0.25 + 0.5 = 0.75 h

  • Step 3: Calculate Average Speed.

    • Average Speed = Total Distance / Total Time = 50 / 0.75 ≈ 66.7 km/h

Part B: Distance-Time Graphs

1. Core Concepts (Short Notes)

• A graph showing an object's distance from a start point over time. Time is on the x-axis, Distance is on the y-axis.

• Gradient (steepness) of the line = Speed.

2. Interpreting the Graph

• Straight, sloped line: Uniform speed.

• Steeper slope: Higher speed.

• Horizontal line (flat): Stationary (not moving, Speed = 0).

• Line sloping down: The object is returning to the starting point.

Part C: Rate of Flow (Volume)

1. Core Concepts (Short Notes)

• This is the same idea as speed, but measures the volume of a liquid that flows in a unit of time.

• Key Formula: Rate of Flow = Volume / Time

2. Exam Tips & Tricks

• Volume Unit Conversion: Questions often mix units to test you. You must know these:

  • 1 litre = 1000 cm³

  • 1 m³ = 1000 litres

• Problem: A tank with a volume of 3 m³ needs to be filled. If water flows in at a rate of 50 litres per minute, how long will it take?

  • Step 1: Convert units to be the same.

    • Volume = 3 m³ = 3 × 1000 = 3000 litres

  • Step 2: Use the formula.

    • Time = Volume / Rate = 3000 litres / 50 litres/min = 60 minutes