Curriculum Alignment
- Strand
- 2.0 Measurements and Geometry
- Sub-Strand
- 2.9 Vectors 1
Subsection 2.9.6 Vectors in Real-Life
Teacher Resource 2.9.86.
To assist your teaching, we have prepared lesson resources, aligned with this textbook and the CBC. The Lesson Plan links to syllabus learning outcomes and provides suggest time allocations. The Step-by-Step Guide provides more detailed guidance on how to teach the content, including suggested questions to ask learners, and possible answers.
In daily life, we describe motion using quantities such as distance, speed and direction. Some quantities depend only on size, while others depend on both size and direction.
A scalar quantity has magnitude only. Examples include distance, time and speed.
A vector quantity has both magnitude and direction. Examples include displacement, velocity and acceleration.
Vectors help us describe motion accurately in transport, sports, navigation and engineering.
Learner Experience 2.9.11.
Materials: Ruler, graph paper
Instructions:
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Draw the movement on a straight line.
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Find the total distance travelled.
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Determine how far the student is from the starting point.
Now suppose the total time taken is \(2 \, \text{hours}\text{.}\)
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Calculate the average speed.
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Calculate the average velocity.
In your group discuss:
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Which quantities depend only on size?
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Which quantities depend on both size and direction?
Key Takeaway 2.9.87.
Distance is the total path travelled. It is a scalar quantity(has only magnitude).
Displacement is the straight-line change in position together with direction. It is a vector quantity (has both magnitude and direction).
Speed is the rate of change of distance.
\begin{equation*}
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\end{equation*}
Speed is a scalar quantity.
Velocity is the rate of change of displacement.
\begin{equation*}
\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}
\end{equation*}
Velocity is a vector quantity.
Acceleration is the rate of change of velocity.
\begin{equation*}
\text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time}}
\end{equation*}
Acceleration is also a vector quantity.
Example 2.9.88.
A cyclist rides \(30 \, \text{km}\) east in \(2 \, \text{hours}\text{.}\) Find:
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the speed,
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the velocity.
Example 2.9.89.
A vehicle increases its velocity from \(8 \, \text{m/s}\) to \(20 \, \text{m/s}\) in \(4 \, \text{s}\text{.}\) Find its acceleration.
Checkpoint 2.9.90.
Checkpoint 2.9.91.
Exercises Exercises
1.
2.
3.
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5.
A runner completes one full lap of \(400 \, \text{m}\) in \(50 \, \text{s}\text{.}\) Find:
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the distance travelled,
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the displacement.
6.
A car changes its velocity from \(15 \, \text{m/s east}\) to \(5 \, \text{m/s east}\) in \(2 \, \text{s}\text{.}\) Find its acceleration.
7.
A cyclist travels \(12 \, \text{km}\) north and then \(9 \, \text{km}\) east. Determine the total distance travelled.
8.
A delivery rider travels \(6 \, \text{km}\) east and then \(8 \, \text{km}\) east in a total time of \(2 \, \text{hours}\text{.}\)
9.
A truck moves \(50 \, \text{km}\) north in \(1 \, \text{hour}\text{,}\) then returns \(20 \, \text{km}\) south in \(0.5 \, \text{hours}\text{.}\)
Find:
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the total distance travelled,
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the displacement,
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the average velocity for the entire journey.
10.
A car accelerates from rest to \(30 \, \text{m/s}\) in \(6 \, \text{s}\text{.}\) Find its acceleration.
