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Mathematics Speed Questions Lecture

Jun 26, 2024

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Mathematics Speed Questions Lecture

Introduction

The instructor aims to help students master speed-related questions as this is a weak topic for many. The session will cover eight types of speed questions. Students should have a piece of paper, a pen or pencil, and a calculator ready.

General House Rules

  • Refrain from chatting nonsensical stuff.
  • Note down any questions and ask them at the end of the session during Q&A.
  • Check your sound system if you can't hear or see properly; recording will be uploaded later.

Topics to be Covered

  1. General Speed Questions
  2. Average Speed
  3. Same Direction, Same Start Time
  4. Same Direction, Different Start Time
  5. Same Direction, Different Start Time with Opening Gap
  6. Moving Towards Each Other, Same Start Time
  7. Moving Towards Each Other, Different Start Time
  8. Moving Away From Each Other, Same Start Time

Key Formulas

  • Distance (D) = Speed (S) x Time (T)
  • Speed (S) = Distance (D) / Time (T)
  • Time (T) = Distance (D) / Speed (S)

1. General Speed Questions

Example Problem

A motorist travels 250 km at 80 km/h, then slows down to 60 km/h for the rest of the journey, taking 3.5 hours.

  • Draw the distance-speed-time timeline.
  • Two parts: first segment with speed = 80 km/h, second with speed = 60 km/h.
  • Use DST formula to find total distance.

Solution

  1. Calculate distance for the second part: Speed x Time = 60 x 3.5 = 210 km
  2. Use timeline to find distances and total distance.
  3. Calculate time and speed conversions if required.

2. Average Speed

Example Problem

Kiran cycles 25 km/h for 10 km, stays at the park for 1 hour 50 min, then returns in 40 min. Find average speed.

  • Convert all times to hours.
  • Calculate total distance and time.

Solution

  1. Distance: 10 km each way, total 20 km.
  2. Time: 24 min + 40 min = 64 min = 1.07 hours.
  3. Average Speed = Distance / Time = 20 km / 1.07 hours = 18.7 km/h

3. Same Direction, Same Start Time

Example Problem

Sharon cycles 4.5 km at 375 m/min, Signe is 600 m behind upon reaching the end.

Solution

  1. Calculate time taken by Sharon: Distance/Speed = 4.5 km / 375 m/min
  2. Adjust speeds to match units (e.g., convert km to meters).

4. Same Direction, Different Start Time

Example Problem

Two vehicles start at different times, one overtakes the other.

Solution

  1. Draw timeline showing start times and gaps.
  2. Calculate time and distance gaps.
  3. Adjust speeds and distances for coherent units.

5. Opening the Gap

Example Problem

John and David start at different times and speeds.

Solution

  1. Calculate speed ratios and adjust time.
  2. Draw distance-speed-time diagrams for clarity.

6. Moving Towards Each Other, Same Start Time

Example Problem

Two vehicles starting from opposite points, moving towards each other.

Solution

  1. Calculate closing speed: sum of individual speeds.
  2. Use distance/time formula to find when they meet.

7. Moving Towards Each Other, Different Start Time

Example Problem

One vehicle starts first, the other later.

Solution

  1. Calculate distances covered at different times.
  2. Adjust timelines for overlapping intervals.

8. Moving Away From Each Other, Same Start Time

Example Problem

Two people start at the same point and go in opposite directions.

Solution

  1. Calculate relative speeds.
  2. Use distances to find when they are a certain length apart.

Conclusion

Mastering the art of drawing distance-speed-time timelines is crucial. Use the provided recording for revisiting and understanding difficult segments.

Full transcript