Grade 10 · Core Mathematics · Lesson 1 of 14

Distance, Displacement, Speed, Velocity and Acceleration

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners distinguish between distance and displacement in practical motion situations.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L140 minutes · 2 slides

KICD learning outcome (a)

Explain the terms distance, displacement, speed, velocity and acceleration in real-life situations.

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

Distinguish between distance and displacement in practical motion situations
Calculate speed and velocity using path length, displacement, and time
Define acceleration and calculate its value from change in velocity and time

Key vocabulary

Displacement: The straight-line distance and direction from an initial position to a final position.; The matatu had a direct displacement of ninety kilometres East from Town A.
Velocity: The rate at which a body changes its displacement over time in a specified direction.; Dividing ninety kilometres East by one point five hours gave a velocity of sixty km/h East.
Acceleration: The rate of change of velocity with respect to time.; The lorry achieved an acceleration of two point five metres per second squared.

Lesson preview

Slide 1 · Distance, Displacement, Speed, and VelocityModel · 18 min

Figure 1: A diagram comparing a winding distance path of 120 km and a straight-line displacement of 90 km East between Town A and Town B.

Distance measures the total path length travelled by an object, regardless of direction, whereas displacement is the net straight-line distance from the starting point to the final position in a specified direction. Speed is the scalar rate at which distance is covered over time, while velocity is the vector rate of change of displacement, including both magnitude and direction. Look at Figure 1 to see the difference between distance and displacement.

Distance is the total length along a path, measured in metres or kilometres.
Displacement is the direct straight-line path from initial to final position with direction.
Speed equals distance divided by time and is measured in m/s or km/h.
Velocity equals displacement divided by time, specifying both speed and direction.

Worked example. Find speed:

Speed = \frac{Distance}{Time} = \frac{120 km}{1.5 h} = 80 km/h

. Find velocity:

Velocity = \frac{Displacement}{Time} = \frac{90 km East}{1.5 h} = 60 km/h East

. Answer: $Speed = 80 km/h$ , $Velocity = 60 km/h East$ .

Check question: A cyclist rides $15 km$ North, then turns and rides $15 km$ South back to the starting point in $1 hour$ . What is the cyclist's speed and velocity?

$Speed = 30 km/h$ , $Velocity = 0 km/h$
$Speed = 0 km/h$ , $Velocity = 30 km/h$
$Speed = 30 km/h$ , $Velocity = 30 km/h$
$Speed = 15 km/h$ , $Velocity = 0 km/h$

Show answer

$Speed = 30 km/h$ , $Velocity = 0 km/h$ . Total distance is $15 + 15 = 30 km$ , so speed is $\frac{30}{1} = 30 km/h$ . Since the cyclist returns to the starting point, the final displacement is $0 km$ , making the velocity $0 km/h$ .

Slide 2 · Understanding and Calculating AccelerationCheck · 22 min

Figure 2: A velocity-time graph showing constant acceleration, where an initial velocity of 15 m/s increases to 35 m/s over 8 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.

Both 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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