Grade 10 · Core Mathematics · Lesson 9 of 14

Interpreting Velocity-Time Graphs in Linear Motion

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners read velocity at a given instant and find the time corresponding to a given velocity from a velocity-time graph.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L940 minutes · 4 slides

KICD learning outcome (f)

Interpret velocity-time graph in different situations.

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

Read velocity at a given instant and find the time corresponding to a given velocity from a velocity-time graph.
Calculate acceleration over specified time intervals from the gradient of graph line segments.
Determine total distance travelled by calculating the area under a velocity-time graph.

Key vocabulary

Velocity-time graph: A plot showing how an object's velocity changes with time along coordinate axes.; We read the vertical height on the velocity-time graph to determine velocity at five seconds.
Gradient: The ratio of vertical change to horizontal change along a straight line section.; The gradient of the segment measures acceleration in metres per second squared.
Instantaneous velocity: The velocity of a moving object at one exact moment in time.; We read the instantaneous velocity at fourteen seconds directly from the y-axis.
Trapezium area: The space inside a four-sided shape with two parallel horizontal boundaries.; Using the trapezium area formula gives the total distance travelled by the motorcycle.
Deceleration: The rate at which an object decreases its velocity over time.; The speed boat experiences deceleration as its velocity drops from thirty to zero.
Displacement: The net change in position of an object in a specific direction.; The total area under the velocity-time graph represents the car's overall displacement.

Lesson preview

Slide 1 · Reading Values and Gradients from a Velocity-Time GraphOpening · 10 min

Figure 1: A velocity-time graph showing a van's motion with constant acceleration, constant velocity, and constant deceleration phases.

A velocity-time graph displays how speed in a specified direction changes over time. We plot time in seconds along the horizontal axis and velocity in metres per second along the vertical axis. By reading points directly off the curve, we can determine the velocity at a precise instant or find when a specific velocity is reached. Furthermore, calculating the gradient of any straight line section reveals the acceleration over that particular time interval.

The vertical axis shows velocity in metres per second, while time is plotted on the horizontal axis.
To find velocity at a given instant, locate time on the horizontal axis and read upwards.
To find time for a given velocity, locate velocity on the vertical axis and read across.
The gradient of a line segment represents acceleration, while zero gradient indicates constant velocity.

Worked example. For (a), the line

O P

connects

(0, 0)

(12, 24)

, so

v = \frac{24}{12} t = 2 t

. At

t = 6 s

v = 2 \times 6 = 12 m/s

. For (b), set

v = 18 m/s

v = 2 t

, which gives

2 t = 18 ⟹ t = 9 s

. For (c), gradient of

O P = \frac{24 - 0}{12 - 0} = 2 {m/s}^{2}

. Answer: (a) $12 m/s$ , (b) $9 s$ , (c) $2 {m/s}^{2}$ .

Check question: Using the van's graph, find the gradient of segment $Q R$ from $Q (32, 24)$ to $R (44, 0)$ and choose the option that correctly states the gradient and its meaning.

$- 2 {m/s}^{2}$ , which represents a deceleration of $2 {m/s}^{2}$
$2 {m/s}^{2}$ , which represents an acceleration of $2 {m/s}^{2}$
$- 0.5 {m/s}^{2}$ , which represents a deceleration of $0.5 {m/s}^{2}$
$- 2 m/s$ , which represents a constant velocity of $2 m/s$

Show answer

$- 2 {m/s}^{2}$ , which represents a deceleration of $2 {m/s}^{2}$ . Gradient $= \frac{0 - 24}{44 - 32} = \frac{- 24}{12} = - 2 {m/s}^{2}$ . A negative gradient on a velocity-time graph indicates deceleration or retardation.

Slide 2 · Key Learning Points: Velocity, Acceleration, and AreaModel · 10 min

Figure 2: A velocity-time graph for a motorcycle courier displaying acceleration, steady speed, and deceleration over a 30-second interval.

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 4 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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