Vectors

​DISTANCE/TIME DIAGRAM - Interactive flash animation to draw graph of the evolution of the distance versus time by driving a moped. Interactive Physics Simulations | Interactive Physics Animations | Physics and Chemistry by a Clear Learning in High School, Middle School, Upper School, Secondary School and Academy. PCCL

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​Segment D: Vectors and Scalars | Georgia Public Broadcasting

Multiple Choice

What is a scalar?

• A scalar is a single numerical value representing magnitude without direction.

• A scalar is a type of matrix used in linear algebra.

• A scalar is a complex number with real and imaginary parts.

• A scalar is a vector with both magnitude and direction.

Explanation Slide...

A scalar is defined as a single numerical value that represents magnitude only, without any associated direction. This distinguishes it from vectors, which have both magnitude and direction.

Multiple Choice

In what scenarios would you use scalars instead of vectors?

• Scalars are preferred for multi-dimensional data analysis.

• Use scalars to represent quantities with direction, like velocity.

• Use scalars when measuring distances in a coordinate system.

• Use scalars when representing single quantities without direction, such as temperature or mass.

Explanation Slide...

Scalars represent single quantities without direction, making them ideal for measuring attributes like temperature or mass. In contrast, vectors include direction, which is unnecessary for these scalar measurements.

Multiple Choice

What is a vector?

• A vector is a type of matrix.

• A vector is a scalar quantity.

• A vector is a quantity defined by both magnitude and direction.

• A vector is a point in space.

Explanation Slide...

A vector is defined by both magnitude and direction, distinguishing it from scalars, which have only magnitude. This makes the correct choice "A vector is a quantity defined by both magnitude and direction."

Multiple Choice

Can you give an example of a real-world application of vectors?

• Navigation systems, such as GPS, use vectors to calculate directions and distances.

• Cooking recipes use vectors to measure ingredient quantities.

• Weather forecasting models use vectors to predict storms.

• Social media algorithms use vectors to analyze user preferences.

Explanation Slide...

Navigation systems like GPS utilize vectors to determine the shortest path and calculate distances between locations, making this the most relevant real-world application of vectors.

Multiple Choice

How do you represent a vector graphically?

• A vector is represented graphically as an arrow.

• A vector is represented as a line segment.

• A vector is represented as a circle.

• A vector is represented as a point.

Explanation Slide...

A vector is represented graphically as an arrow because it has both magnitude and direction. The length of the arrow indicates the vector's magnitude, while the arrowhead shows the direction.

Multiple Choice

What is the main difference between a scalar and a vector?

• Scalars have magnitude only; vectors have both magnitude and direction.

• Scalars are always positive; vectors can be negative.

• Scalars can be represented as arrows; vectors cannot.

• Scalars have direction only; vectors have magnitude and direction.

Explanation Slide...

The correct choice states that scalars have magnitude only, while vectors possess both magnitude and direction. This distinction is fundamental in physics and mathematics, where scalars are quantities like temperature, and vectors include forces.

​What Are Distance and Displacement? | Physics in Motion - YouTube

Multiple Choice

Which of these has a further distance?

• red line
• green line
• they are equal

Multiple Choice

• A

• B

• C

• D

Multiple Choice

You go on a hike on the blue path from point A to point B What distance did you travel

• 4.6 km

• 9.2 km

• 10.3 km

• 0 km

Multiple Choice

You go on a hike on the blue path from point A to point B. What is your displacement

• 4.6 km

• 9.2 km

• 10.3 km

• 0 km

Multiple Choice

From the figure, what is the displacement?

• 20 meters

• 25 meters

• 15 meters

• 25 meters NE

Multiple Choice

Joe rides his bike from point A to point B and then on to point C. What is the total distance traveled?

• 12 m

• 8 m

• 7 m

• 9 m

Multiple Choice

The change in an objects position from the final position to initial position.

• displacement

• distance

• motion

• reference point

Multiple Choice

The sum of all movements from start to the end of motion is best described as____.

• distance

• displacement

• motion

• donkey

​Segment E: Graphical Resolution of Vectors | Georgia Public Broadcasting

​

—What are 2 methods of measuring vectors?

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Draw

Draw a labelled diagram for the following question. Calculate the Distance & Displacement, You must include units and a direction (For Displacement) with your answer

Ray runs 30m North, then 30m West, then 30m South

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Draw

Draw a labelled diagram for the following question. Calculate the Distance & Displacement, You must include units and a direction (For Displacement) with your answer

Amy runs 2 km South then turns around and runs 3 km North.

​Segment F: Mathematical Resolution of Vector | Georgia Public Broadcasting

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Mathematical Resolution of Vector

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Mathematical Resolution of Vector

Multiple Choice

Bill runs 400 meters to Andy's house, turns around, and runs 400 meters back home.  What is Bill's distance?

• 0 meters
• 400 meters
• 800 meters
• 1600 meters

Fill in the Blank

Anthony walks to the pizza place for lunch. He walks 1.0 km East, then 1.5 km South, and then 1.5 km East again. What is his displacement?

Show your work. Include units in your answer. Leave the answer in Km

(

+

.

)

+

(

-

.

)

+

(

+

.

)

=

+

.

.

Fill in the Blank

Anthony walks to the pizza place for lunch. He walks 1.0 km East, then 1.5 km South, and then 1.5 km East again. What distance did he cover?

Show your work. Include units in your answer. Leave the answer in Km

.

+

.

+

.

=

.

Multiple Choice

A car travels 90 meters due north. Then the car turns around and travels 40 meters due south. What is the magnitude and direction of the car's resultant displacement?

• 40 meters, South

• 50 meters, South

• 50 meters, North

• 40 meters, North

Multiple Choice

A persons walks 50 meters directly north, stops, and then travels 32 meters directly south.  What is their distance traveled?

• 82 meters
• 18 meters north

• 18 meters south

Multiple Choice

If a car moves 12 km North, 19 km South, and 12 km North, what is its displacement?

• 12 km
• 19 km [S]

• 5 km [N]

• 5 km [S]

​Segment B: Speed and Velocity | Georgia Public Broadcasting

Khan Academy

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