Grade 10 · Core Mathematics · Lesson 6 of 14

Interpreting Displacement-Time Graphs in Different Situations

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners read displacement at specific times and determine times corresponding to given displacements from displacement-time graphs.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L640 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

Read displacement at specific times and determine times corresponding to given displacements from displacement-time graphs.
Identify intervals of rest, highest velocity, and lowest velocity from graph gradients.
Calculate and convert velocities into requested units such as km/h and m/s from multi-stage motion graphs and tables.

Key vocabulary

Interpolation: Estimating an unknown value between two known data points on a line graph.; We used interpolation to find the displacement of the ship at 15 minutes.
Gradient: The measure of steepness of a line segment calculated as vertical change over horizontal change.; The gradient of the graph between two clock times gives the ship velocity.
Negative Velocity: Velocity of an object moving in the direction opposite to the chosen positive reference direction.; The returning cargo ship had a negative velocity of minus twelve metres per second.

Lesson preview

Slide 1 · Interpreting Maritime Displacement-Time GraphsOpening · 12 min

Figure 1: A displacement-time graph of a ferry journey, showing stationary periods as horizontal lines and movement as sloped lines.

Interpreting displacement-time graphs for maritime journeys involves reading linear segments to extract physical quantities. On a plot of displacement against clock time, horizontal lines represent periods where a vessel is docked or stationary at a port. Sloped lines show motion, where the gradient equals velocity. By analysing specific time intervals—such as between 3:00 pm and 5:00 pm—we can determine both intermediate displacements and precise times when target distances are reached.

A horizontal segment on a displacement-time graph indicates zero velocity and that the vessel is at rest.
Gradient of any straight segment gives the constant velocity of the vessel during that specific time interval.
Displacement at any clock time is read directly from the vertical axis corresponding to that time.
To find when a specific displacement is reached, locate the value on the vertical axis and read across.

Worked example. From 12:00 pm to 2:00 pm (

t = 0

t = 2 h

), velocity

v = \frac{80 - 0}{2 - 0} = 40 km/h

. At 1:00 pm (

t = 1 h

), displacement

s = 40 km

. Between 3:00 pm and 5:00 pm (

t = 3

t = 5 h

), velocity

v = \frac{180 - 80}{5 - 3} = \frac{100}{2} = 50 km/h

. To reach 120 km from 80 km requires

Δ s = 40 km

. Time required

Δ t = \frac{40}{50} = 0.8 h = 48 minutes

. Time is 3:48 pm. Answer: (a) $40 km$ , (b) 3:48 pm, (c) $50 km/h$ .

Check question: Using the ferry journey graph, find the velocity between 12:00 noon and 2:00 pm, and state the displacement of the ferry at 2:30 pm.

Velocity = $40 km/h$ ; Displacement = $80 km$
Velocity = $80 km/h$ ; Displacement = $80 km$
Velocity = $40 km/h$ ; Displacement = $120 km$
Velocity = $0 km/h$ ; Displacement = $80 km$

Show answer

Velocity = $40 km/h$ ; Displacement = $80 km$ . Between 12:00 pm and 2:00 pm, $Δ s = 80 - 0 = 80 km$ over $2 h$ , giving $v = 40 km/h$ . At 2:30 pm, the ferry is stationary during its rest period (between 2:00 pm and 3:00 pm), so its displacement remains $80 km$ .

Slide 2 · Analysing Rest Periods, Maximum, and Minimum VelocitiesModel · 14 min

Figure 2: A multi-stage displacement-time graph showing changing positive slopes, a horizontal rest period, and a negative slope.

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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