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Grade 10 · Core Mathematics · Lesson 12 of 14

Relative Speed in Linear Motion: Advanced Applications

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners calculate overtaking time and clock time when one moving body has a head start.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L1240 minutes · 3 slides

KICD learning outcome (g)

Determine relative speed of two moving bodies in different situations.

By the end of this lesson, learners should be able to

  1. Calculate overtaking time and clock time when one moving body has a head start.
  2. Determine clearance distance and time taken for extended bodies, such as trains, to pass each other.
  3. Solve real-world relative speed problems involving opposite and same direction motion with unit conversions.

Key vocabulary

Head start
The initial distance advantage gained by an object that departs before another object.
The lorry gained a 50 km head start before the car began its pursuit.
Overtaking time
The duration required for a faster object to catch up to a slower object.
The overtaking time of 2 hours was calculated from the head start and relative speed.
Clearance distance
The total distance two extended bodies must move relative to each other to pass fully.
The clearance distance of 400 m was the sum of both train lengths.
Meeting time
The exact moment or time interval when two approaching objects cross paths.
The meeting time was determined as 10:45 am after 2.5 hours of travel.

Lesson preview

Slide 1 · Delayed Departures and Overtaking TimesOpening · 12 min
A diagram illustrating the positions and speeds of a car and a lorry to find their overtaking time and location.
Figure 1: A diagram illustrating the positions and speeds of a car and a lorry to find their overtaking time and location.

When one vehicle departs earlier than another, it gains a distance head start before the second vehicle begins moving. To find when the faster vehicle overtakes the slower one, first calculate this head start distance. Next, divide the head start distance by the relative speed of the two vehicles moving in the same direction. Adding this travel duration to the second vehicle's departure time yields the exact clock time of overtaking.

  • Calculate head start distance by multiplying the earlier vehicle's speed by the difference in departure times.
  • Determine relative speed in the same direction by subtracting the slower speed from the faster speed.
  • Find overtaking time by dividing the head start distance by the calculated relative speed.
  • Add the overtaking time to the later departure time to determine the exact clock time.
Worked example. Calculate departure time difference: 8:00 am−7:00 am=1 hour. Calculate lorry's head start distance: 50 km/h×1 h=50 km. Calculate relative speed in same direction: 75 km/h−50 km/h=25 km/h. Calculate time needed to overtake: Time=50 km25 km/h=2 hours. Determine overtaking clock time: 8:00 am+2 hours=10:00 am. Calculate distance from Kisumu: 75 km/h×2 h=150 km. Answer: The car overtakes the lorry at 10:00 am, at a distance of 150 km from Kisumu..

Check question: A cyclist leaves Kapsabet at 6:30 am travelling at 15 km/h. A matatu departs Kapsabet at 7:30 am along the same road at 60 km/h. At what exact clock time does the matatu overtake the cyclist?

  1. 6:50 am
  2. 7:42 am
  3. 7:45 am
  4. 7:50 am
Show answer

7:50 am. Head start distance =1 h×15 km/h=15 km. Relative speed =60−15=45 km/h. Time taken =1545 h=13 h=20 minutes. Overtaking time =7:30 am+20 minutes=7:50 am.

Slide 2 · Relative Motion for Bodies of Significant LengthModel · 14 min
A diagram of two trains passing each other in opposite directions, showing their individual lengths and converted speeds.
Figure 2: A diagram of two trains passing each other in opposite directions, showing their individual lengths and converted speeds.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • All 3 slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 13 lessons in this sub-strand
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All 14 lessons in Linear Motion

  1. 1Distance, Displacement, Speed, Velocity and AccelerationExplain the terms distance, displacement, speed, velocity and acceleration in real-life situations
  2. 2Determining Velocity and AccelerationDetermine velocity and acceleration in different situations
  3. 3Determining Velocity and Acceleration in Different SituationsDetermine velocity and acceleration in different situations
  4. 4Drawing Displacement-Time Graphs in Linear MotionDraw a displacement-time graph of different situations
  5. 5Interpreting Displacement-Time GraphsInterpret displacement-time graph in different situations
  6. 6Interpreting Displacement-Time Graphs in Different SituationsInterpret displacement-time graph in different situations
  7. 7Drawing Velocity-Time Graphs from Data TablesDraw a velocity-time graph from given tables in different situations
  8. 8Drawing Velocity-Time Graphs from Data Tables: Deceleration and ScenariosDraw a velocity-time graph from given tables in different situations
  9. 9Interpreting Velocity-Time Graphs in Linear MotionInterpret velocity-time graph in different situations
  10. 10Interpreting Velocity-Time Graphs in Practical SituationsInterpret velocity-time graph in different situations
  11. 11Relative Speed in Linear MotionDetermine relative speed of two moving bodies in different situations
  12. 12Relative Speed in Linear Motion: Advanced ApplicationsDetermine relative speed of two moving bodies in different situations
  13. 13Appreciating Linear Motion in Real-Life SituationsAppreciate use of linear motion in real-life situations
  14. 14Real-Life Applications of Linear MotionAppreciate use of linear motion in real-life situations