PU3L2: Distance & Displacement (Draft)

Nora and David are planning a hiking trip. They start at the base of a hill and walk 3 km north, then 4 km east. What is the resultant vector of their journey?

• A scalar quantity that tells the length of a path taken by an object

• The numerical value, with associated units, of magnitude

• The vector representing the displacement when two or more vectors are added together

• Size or amount

Answer explanation

The correct choice is the vector representing the displacement when two or more vectors are added together. Nora and David's journey can be represented as a vector sum of their north and east movements, resulting in their overall displacement.

Ava is pushing a shopping cart at the grocery store. What does the term 'vector' include in this context?

• Only magnitude

• Only direction

• Magnitude and direction

• Only size

Answer explanation

In this context, a 'vector' refers to a quantity that has both magnitude (how much) and direction (where to). Therefore, the correct answer is 'Magnitude and direction', as both aspects are essential to define the vector of Ava's push.

Abigail is walking in a park. In the example, what is the vector quantity?

• 0.5 m/s

• 1 m/s

• 0.5 m/s north

• 1 m/s south

Answer explanation

The vector quantity includes both magnitude and direction. Among the options, '0.5 m/s north' specifies a speed and direction, making it a vector. The other choices only provide speed, which are scalar quantities.

Charlotte and Henry are walking from their school to the park. What is the main difference between the distance they walk and their displacement?

• Distance includes direction, displacement does not

• Displacement includes direction, distance does not

• Both include direction

• Neither includes direction

Answer explanation

The main difference is that displacement includes direction, indicating the shortest path from start to end, while distance is the total length of the path walked, regardless of direction.

Elijah is standing at the origin of a coordinate plane. What are the coordinates of his starting point?

• (0, 0)

• (4, 2)

• (2, 4)

• (1, 1)

Answer explanation

Elijah is at the origin of the coordinate plane, which is defined as the point where both x and y coordinates are zero. Therefore, his starting point is (0, 0).

Mason is planning a road trip and checks his car's odometer before leaving his house. What is the odometer reading?

• 10,000 miles

• 10,326 miles

• 10,500 miles

• 10,250 miles

Answer explanation

Mason's odometer reading is 10,326 miles, which indicates the total distance traveled by the car. This choice is the most specific and likely reflects the current mileage before his road trip.

William is walking along a path from his house to the park. What is the distance of segment FG in the path from point A to point G?

• 3/4 mile

• 5/4 mile

• 9/4 mile

• 2/4 mile

Answer explanation

To find the distance of segment FG from point A to point G, we add the distances along the path. The total distance is 9/4 mile, which is the correct answer.

Avery is walking from point A to point B, then to point G. Which segment represents the magnitude of the displacement vector in Avery's journey?

• Segment AB

• Segment AG

• Segment AC

• Segment AH

Answer explanation

The displacement vector represents the shortest distance from the starting point A to the final point G. Therefore, Segment AG is the correct choice, as it directly connects these two points.

Benjamin is walking from his house to the park. What is the shortest distance between his house and the park in a straight line called?

• Distance

• Speed

• Displacement

• Velocity

Answer explanation

The shortest distance between two points, like Benjamin's house and the park, is called displacement. It refers to the straight line connecting the two locations, regardless of the path taken.

Noah is planning a round trip to visit his friend. What additional information is needed to find the total distance of his round trip?

• Circumference of a circle

• Area of a triangle

• Volume of a sphere

• Perimeter of a square

Answer explanation

To find the total distance of Noah's round trip, we need the circumference of the circle representing the route. The other options (area, volume, perimeter) are not relevant to calculating distance.