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Grade 10 · Core Mathematics · Lesson 5 of 14

Interpreting Displacement-Time Graphs

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners read displacement and time values directly from displacement-time graphs.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L540 minutes · 3 slides

KICD learning outcome (d)

Interpret displacement-time graph in different situations.

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

  1. Read displacement and time values directly from displacement-time graphs.
  2. Determine velocity as the gradient of displacement-time line segments.
  3. Interpret stationary, forward, and return stages in linear motion graphs.

Key vocabulary

Displacement
Distance and direction of an object from a specified fixed origin point.
The matatu reached a displacement of 50 km from Nairobi at 9:00 am.
Gradient
The ratio of vertical change to horizontal change along a straight graph line.
The gradient of segment AB is 50 km/h, representing velocity during that hour.
Velocity
Rate of change of displacement with respect to time, including direction.
The drone has a negative velocity of -5 m/s when returning towards origin.

Lesson preview

Slide 1 · Introduction to Displacement-Time GraphsOpening · 12 min
A displacement-time graph illustrating the motion of a delivery matatu from 8:00 am to 12:00 noon.
Figure 1: A displacement-time graph illustrating the motion of a delivery matatu from 8:00 am to 12:00 noon.

A displacement-time graph shows how far an object has moved from a chosen starting point over time. From this graph, we can directly read the displacement at any given time or determine the precise time corresponding to a specific displacement. Furthermore, calculating the gradient of each straight segment gives the velocity of the object during that time interval. A horizontal line segment indicates that the object is stationary.

  • The vertical axis represents displacement from an origin, while the horizontal axis represents time elapsed.
  • Direct reading gives the position of a body at any instant or time for a position.
  • The gradient of a displacement-time line segment equals the constant velocity during that period.
  • A horizontal segment on a displacement-time graph shows zero gradient, meaning the object is at rest.
Worked example. At 9:30 am, time lies on horizontal segment BC where displacement remains constant at 50 km. Segment CD rises from 50 km at 10:00 am to 110 km at 12:00 noon. Velocity on CD is 110−5012−10=602=30 km/h. The velocity on segment CD is 30 km/h, which is below the 40 km/h speed limit. Therefore, the driver acted responsibly. Answer: (a) 50 km, (b) 30 km/h, Yes, the driver acted responsibly.

Check question: From the matatu graph, what is the velocity of the matatu between 8:00 am and 9:00 am (segment AB)?

  1. 50 km/h
  2. 50 m/s
  3. 25 km/h
  4. 0 km/h
Show answer

50 km/h. Between 8:00 am and 9:00 am (1 hour elapsed), displacement increases from 0 km to 50 km. Velocity = 50−01−0=50 km/h.

Slide 2 · Analysing Multi-Stage Motion GraphsModel · 14 min
A displacement-time graph representing a drone's multi-stage motion over a period of 20 seconds.
Figure 2: A displacement-time graph representing a drone's multi-stage motion over a period of 20 seconds.

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