Grade 10 · Core Mathematics · Lesson 2 of 14

Determining Velocity and Acceleration

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners determine velocity as the ratio of displacement to time in a specified direction.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L240 minutes · 3 slides

KICD learning outcome (b)

Determine velocity and acceleration in different situations.

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

Determine velocity as the ratio of displacement to time in a specified direction.
Investigate changing velocity using an inclined surface and define acceleration.
Calculate acceleration by dividing the difference in velocity by the elapsed time.

Key vocabulary

Velocity: The displacement per unit time recorded in a specific direction.; A cyclist travelling 300 metres North in 50 seconds achieves a velocity of 6 m/s.
Displacement: The straight distance and direction from a starting point to a final position.; Running 200 metres directly East creates a displacement of 200 metres due East.
Acceleration: The variation of velocity per unit time during a specified duration.; A trolley increasing speed down an inclined track undergoes constant positive acceleration.
Initial velocity: The velocity of a moving body at the beginning of an observed interval.; A runner starting at 3 m/s East has an initial velocity of 3 m/s.
Final velocity: The velocity of a moving object at the end of a given time.; A bus reaching 15 m/s after accelerating has a final velocity of 15 m/s.

Lesson preview

Slide 1 · Understanding Velocity and DisplacementOpening · 12 min

Figure 1: A diagram showing a displacement of 650 metres South alongside a stopwatch indicating 130 seconds.

Velocity measures how fast an object moves in a given direction. Unlike speed, which only considers total distance, velocity depends on displacement, which is the straight distance towards a specific direction. To determine velocity, we calculate the ratio of displacement to time duration. For instance, measuring a distance of 120 metres along a direct easterly path across school grounds and measuring duration allows us to calculate the learner's precise velocity in metres per second. Use Figure 1 to see how to represent displacement and time for your calculations.

Velocity is defined as the ratio of displacement to time in a specified direction.
Displacement measures the straight-line distance and direction from the starting point.
The SI unit for measuring velocity is metres per second, written as m/s.
Dividing straight line displacement by total elapsed time yields average velocity.

Worked example. Identify displacement:

Displacement = 650 m towards South

. Identify duration:

Time = 130 s

. Apply the velocity formula:

Velocity = \frac{Displacement}{Time}

. Calculate:

Velocity = \frac{650 m}{130 s} = 5 m/s towards South

. Answer: $5 m/s towards South$ .

Check question: An athlete runs along a straight track measuring $180 m$ due East in $24 seconds$ . What is the athlete's velocity?

$7.5 m/s due East$
$7.5 m/s$
$4320 m/s due East$
$0.13 m/s due East$

Show answer

$7.5 m/s due East$ . Velocity is displacement divided by time, so $\frac{180 m}{24 s} = 7.5 m/s due East$ .

Slide 2 · Investigating Acceleration on an Inclined SurfaceModel · 14 min

Figure 2: A trolley starting from rest and rolling down a 3-metre inclined wooden board to the finish.

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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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Determining Velocity and Acceleration

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

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 14 lessons in Linear Motion