Skip to content
Request a demo

Grade 10 · Core Mathematics · Lesson 11 of 14

Relative Speed in Linear Motion

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners determine the relative speed of two bodies moving towards each other in opposite directions.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L1140 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. Determine the relative speed of two bodies moving towards each other in opposite directions
  2. Determine the relative speed of two bodies moving in the same direction
  3. Calculate the time taken for two moving bodies to meet or overtake using relative speed

Key vocabulary

Relative speed
The speed at which the distance between two moving bodies changes over time.
The relative speed of two approaching cars is the sum of their individual speeds.
Overtaking time
The duration needed for a faster body to catch up and pass a slower body.
We calculate the overtaking time by dividing the separation gap by the relative speed.
Head start
The initial distance advantage gained by an object that departs before another object.
A two-hour head start at fifteen kilometres per hour creates a thirty kilometre gap.

Lesson preview

Slide 1 · Relative Speed of Approaching BodiesOpening · 12 min
Two minibuses travelling towards each other from Nakuru and Naivasha demonstrate how relative speed is calculated by adding their individual speeds.
Figure 1: Two minibuses travelling towards each other from Nakuru and Naivasha demonstrate how relative speed is calculated by adding their individual speeds.

When two moving bodies travel towards one another from opposite starting points, the rate at which the distance between them decreases is the sum of their individual speeds. This rate is called their relative speed. To find the total time required for the two bodies to meet, divide the initial distance separating them by their relative speed. Use Figure 1 to visualise adding the speeds of bodies moving towards each other.

  • Bodies travelling towards one another close the distance gap faster than a stationary body would.
  • The relative speed of two bodies moving in opposite directions equals the sum of their speeds.
  • Dividing the total separation distance by the relative speed gives the duration required to meet.
  • Always convert time units consistently to hours, minutes, or seconds when calculating meeting times.
Worked example. Calculate relative speed by adding individual speeds: Relative Speed = 70 km/h+50 km/h=120 km/h. Calculate time to meet using T=DistanceRelative Speed=80 km120 km/h=23 hours. Convert hours to minutes: 23×60 minutes=40 minutes. Answer: Relative speed is 120 km/h and time taken to meet is 40 minutes (0.67 hours)..

Check question: Two runners start 180 m apart on a straight track and head towards one another at 5 m/s and 4 m/s. How many seconds pass before they meet?

  1. 20 seconds
  2. 36 seconds
  3. 45 seconds
  4. 180 seconds
Show answer

20 seconds. When objects move towards each other, their relative speed is the sum of their individual speeds: 5 m/s+4 m/s=9 m/s. The time taken to meet is the initial distance divided by the relative speed: 180 m9 m/s=20 seconds.

Slide 2 · Relative Speed in the Same DirectionModel · 14 min
A faster car catching up to a slower lorry shows that relative speed in the same direction is the difference between their speeds.
Figure 2: A faster car catching up to a slower lorry shows that relative speed in the same direction is the difference between their 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
See the school projectorWhatsApp us

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