Lesson Notes By Weeks and Term v3 - Senior Secondary 1
Position, Distance and Displacement
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Position, Distance and Displacement
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Subject: Physics
Class: Senior Secondary 1
Term: 3rd Term
Week: 2
Theme: Interaction Of Matter, Space And Time
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This topic introduces fundamental concepts in kinematics, the branch of mechanics that describes the motion of points, bodies, and systems of bodies without considering the forces that cause them to move. Understanding how to precisely describe an object's location and its change in location is crucial for further studies in physics and various real-world applications. Nigerian learners frequently encounter these concepts in their daily lives, from navigating between towns, describing journeys, or understanding the movement of vehicles and people in their communities.
Performance Objectives:
This section provides a detailed explanation of position, distance, and displacement, along with necessary prerequisite concepts. 2.
1. Reference Point: To describe the position of an object, a reference point (or origin) is essential. This is a fixed location from which all other positions are measured. For instance, to describe the position of a student in a classroom, the teacher's desk or the classroom door could serve as a reference point. 2.
2. Position: Position refers to the location of an object with respect to a chosen reference point. It is a vector quantity, meaning it has both magnitude (how far) and direction (where).
Example: If the school gate is the reference point, a student's position might be "50 meters North of the school gate." 2.
3. Scalar and Vector Quantities: Before defining distance and displacement, it is crucial to understand the difference between scalar and vector quantities.
Scalar Quantity: A physical quantity that has magnitude only. It does not require direction for its complete description.
Examples: Mass (e.g., 50 kg), time (e.g., 2 hours), temperature (e.g., 30°C), speed (e.g., 60 km/h), and distance.
Vector Quantity: A physical quantity that has both magnitude and direction. Both are necessary for its complete description.
Examples: Force (e.g., 10 N downwards), velocity (e.g., 80 km/h North), acceleration (e.g., 9.8 m/s2 downwards), and displacement. 2.
4. Distance: Distance is the total length of the actual path covered by an object during its motion, irrespective of the direction of travel. It is a scalar quantity. It is always a positive value and cannot be zero unless the object has not moved. The SI unit of distance is the meter (m).
Example: A student walks from home to the market, then from the market to school. The distance covered is the sum of the length of the path from home to market and the length of the path from market to school. 2.
5. Displacement: Displacement is the shortest straight-line distance between an object's initial position and its final position, along with the direction. It is the change in position of an object. It is a vector quantity. It has both magnitude and direction. It can be positive, negative, or zero.
Positive/Negative: Indicates direction (e.g., +5m might mean 5m East, -5m would mean 5m West if East is defined as positive).
Zero: If an object returns to its starting point, its final displacement is zero, even if it has covered a significant distance. The SI unit of displacement is the meter (m).
Example: If a student walks from home to the market and then back to their home, their final displacement is zero, even though they covered a certain distance. 2.
6. Distinguishing Between Distance and Displacement: | Feature | Distance | Displacement | | :-------------- | :----------------------------------------- | :--------------------------------------------- | | Quantity Type | Scalar (magnitude only) | Vector (magnitude and direction) | | Path Dependence | Depends on the actual path taken | Depends only on initial and final positions | | Value | Always positive | Can be positive, negative, or zero | | Nature | Total length of the journey | Shortest straight-line path between two points | | Example | Odometer reading in a vehicle | Straight-line distance on a map with direction | 2.
7. Translational Motion: Translational motion refers to motion where an object changes its position without any rotation. This lesson focuses on describing distance and displacement within this context. --- Worked Examples (Nigerian Context): Example 1 (One-Dimensional Motion): A Keke Napep driver starts from a bus stop in Ibadan. He drives 8 km North to Bodija Market, then turns around and drives 3 km South towards the bus stop. a) What is the total distance covered by the Keke Napep? b) What is the final displacement of the Keke Napep from the bus stop?
Solution: Let's assume North is the positive direction. a)
Distance: Distance is the total path covered. Distance = (Path North) + (Path South) Distance = 8 km + 3 km Distance = 11 km b)
Displacement: Displacement is the change in position from the start, considering Ibadan. He drives 8 km North to Bodija Market, then turns around and drives 3 km South towards the bus stop. a) What is the total distance covered by the Keke Napep? b) What is the final displacement of the Keke Napep from the bus stop?
Solution: Let's assume North is the positive direction. a)
Distance: Distance is the total path covered. Distance = (Path North) + (Path South) Distance = 8 km + 3 km Distance = 11 km b)
Displacement: Displacement is the change in position from the start, considering direction. Displacement = (Initial path in North direction) + (Subsequent path in South direction) Displacement = +8 km + (-3 km) (since South is opposite to North, it's negative) Displacement = 5 km North The final displacement is 5 km in the North direction from the starting bus stop. Example 2 (Two-Dimensional Motion - Perpendicular Paths): A market woman in Onitsha walks 60 meters East from her stall to buy some fresh produce, then turns and walks 80 meters North to deliver them to a customer. a) What is the total distance covered by the market woman? b) What is her displacement from her starting stall?
Solution: a)
Distance: Distance = (Path East) + (Path North) Distance = 60 m + 80 m Distance = 140 m b)
Displacement: The woman's path forms a right-angled triangle where the displacement is the hypotenuse. Let the starting stall be A, the produce point be B, and the customer's point be C. AB = 60 m (East), BC = 80 m (North). We need to find AC (magnitude) and its direction. Magnitude of Displacement (AC) = $\sqrt{(AB)^2 + (BC)^2}$ (Using Pythagoras theorem) Magnitude of Displacement = $\sqrt{(60 m)^2 + (80 m)^2}$ Magnitude of Displacement = $\sqrt{3600 m^2 + 6400 m^2}$ Magnitude of Displacement = $\sqrt{10000 m^2}$ Magnitude of Displacement = 100 m Direction: The displacement is in the North-East direction from her starting stall. To be more precise, the angle $\theta$ North of East can be found using trigonometry: $\tan(\theta) = \frac{Opposite}{Adjacent} = \frac{BC}{AB} = \frac{80}{60} = \frac{4}{3}$ $\theta = \arctan(\frac{4}{3}) \approx 53.1^\circ$ So, the displacement is 100 m at $53.1^\circ$ North of East from her starting stall.
Example 3 (Zero Displacement): A student cycles from their home in Lekki to their school in Ikoyi, a distance of 10 km along a straight road. After school, the student cycles back home along the same road. a) What is the total distance covered by the student? b) What is the final displacement of the student from their home?
Solution: a)
Distance: Distance = (Distance to school) + (Distance back home) Distance = 10 km + 10 km Distance = 20 km b)
Displacement: The student started at home and returned to home. Their initial and final positions are the same.
Therefore, the final displacement is 0 km. This section outlines practical activities for both teachers and students to facilitate understanding. 3.
1. Teacher Activities: Introduction (Engage): Begin by asking students about a familiar journey, e.g., "How far is your house from school?" and "If you had to fly directly like a bird, would that distance be the same as the road you take?" This sparks discussion on path vs. straight line.
Concept Definition: Introduce and define reference point, position, scalar, vector, distance, and displacement using clear language and simple analogies. Write key terms on the board.
Visual Aids: Draw diagrams on the board to illustrate different paths taken and the resulting distance vs. displacement (e.g., a person walking around a rectangular field, a zigzag path). Use a large map of Nigeria or a local area map to point out two cities (e.g., Kano and Abuja). Ask students to imagine the road distance vs. a direct flight path.
Demonstration (Practical Measurement): In the classroom, mark a starting point (A) and an ending point (B). Walk a winding path from A to B (e.g., around tables). Use a measuring tape to measure the length of this winding path (distance). Then, use the same measuring tape to measure the straight-line distance directly from A to B (magnitude of displacement). Point out the direction. Mark a point C. Walk from A to B, then from B to C, and then back from C to
A. Measure the total distance and discuss the final displacement (zero).
Guided Problem Solving: Work through the "Worked Examples" (Section 2.7) step-by-step on the board, encouraging student participation in each step. Emphasize vector notation and direction for displacement.
Questioning: Regularly ask probing questions to check for understanding (e.g., "Can distance ever be zero if an object moves?", "When is displacement equal to distance?"). 3.
2. Student Activities: Brainstorming: In small groups, students list 3-5 examples of scalar quantities and 3-5 examples of vector quantities they encounter in daily life. Share and discuss as a class.
Classroom Measurement Activity: Students work in small groups (e.g., 3-4 students). Provide each group with a measuring tape or meter rule.
Task 1: Select two distinct points in the classroom (e.g., the teacher's desk and the classroom door). One student walks a zigzag path between these points while another student uses the tape to measure the approximate length of this path (distance). A third student then measures the straight-line path directly between the two points (magnitude of displacement). Students record their findings and note the directions.
Task 2: Select a point (e.g., their own desk). Walk to another point, then to a third point, and then back to their starting desk. Students discuss and record the total distance covered and the final displacement.
Diagramming Motion: Students draw simple diagrams to represent various scenarios of motion (e.g., a person walking North, then East) and clearly label the distance and displacement.
Problem Solving: Attempt the guided practice questions individually or in pairs, then discuss solutions as a class.
Group Discussion: Discuss real-life situations where distinguishing between distance and displacement is important (e.g., a pilot navigating, a delivery driver, a surveyor). These questions are designed to reinforce understanding, with step-by-step solutions for the teacher.
Question 1: A student living in Yaba, Lagos, walks 500 m East from their home to a junction. From the junction, they then walk 300 m West towards a shop. a) What is the total distance covered by the student? b) What is the final displacement of the student from their home?
Solution: a)
Total Distance Covered: Distance is the sum of all path lengths. Distance = 500 m (East) + 300 m (West) Distance = 800 m b)
Final Displacement: Assume East is the positive direction. West is then the negative direction. Displacement = (Initial path) + (Subsequent path) Displacement = +500 m + (-300 m) Displacement = 200 m The final displacement is 200 m East from their home.
Question 2: An Okada rider travels 12 km North from a village to the nearest town. From the town, he then travels 9 km East to deliver a package to a remote settlement. a) What is the total distance covered by the Okada rider? b) What is the magnitude of the Okada rider's displacement from the village to the remote settlement? c) In what general direction is the Okada rider's displacement?
Solution: a)
Total Distance Covered: Distance = 12 km (North) + 9 km (East) Distance = 21 km b)
Magnitude of Displacement: The North and East movements are perpendicular, forming a right-angled triangle. Magnitude of Displacement = $\sqrt{(12 km)^2 + (9 km)^2}$ Magnitude of Displacement = $\sqrt{144 km^2 + 81 km^2}$ Magnitude of Displacement = $\sqrt{225 km^2}$ Magnitude of Displacement = 15 km c)
Direction of Displacement: The displacement is in the North-East direction from the village.
Question 3: A vendor pushes a wheelbarrow of goods 20 meters forward from her starting point, then turns around and pushes it 20 meters backward to her exact starting point. a) What is the total distance covered by the wheelbarrow? b) What is the final displacement of the wheelbarrow from its starting point?
Solution: a)
Total Distance Covered: Distance = 20 m (forward) + 20 m (backward) Distance = 40 m b)
Final Displacement: The wheelbarrow returned to its exact starting point.
Therefore, the final displacement is 0 m.
Question 4: Explain a scenario in Nigerian daily life where the distance travelled would be much greater than the displacement, and another scenario where they could be almost equal.
Solution: Distance much greater than Displacement: A driver navigating through the heavily congested streets of Lagos Island from CMS to Apongbon. The actual road taken involves many turns, traffic, and detours, covering a long distance.
However, the direct straight-line displacement from CMS to Apongbon (perhaps across the lagoon or through less congested inner roads) would be much shorter.
Distance almost equal to Displacement: A direct flight from Lagos to Abuja. Although the plane takes a specific path, if the flight is direct and without significant detours due to weather or air traffic, the actual path length (distance) covered by the aircraft would be very close to the straight-line displacement between the two cities.
Urban Planning and Transportation in Nigeria: Application: When planning new road networks in rapidly expanding Nigerian cities like Abuja or Port Harcourt, engineers consider the desired displacement between two key areas to achieve efficient transport links.
However, the actual construction involves following terrain, existing structures, and land acquisition, resulting in a road that covers a greater distance. For public transportation, efficient routing (minimizing displacement) saves time, while fuel consumption is calculated based on distance.
Example: Constructing an overhead bridge or flyover (e.g., in Lagos or Onitsha) often aims to reduce travel time by creating a more direct path, effectively reducing displacement and sometimes distance by avoiding ground-level obstacles. Agriculture and Surveying in Rural Nigeria: Application: In rural communities, farmers or community leaders might need to describe the size of a plot of land or the location of a water source relative to a village. Surveyors use displacement (straight-line measurements with direction) to accurately map land boundaries, define property lines, and plan irrigation channels. The total distance a farmer might walk around their farm during a day is much more than their displacement from home to the farm at any given time.
Example: A surveyor using a GPS device to plot boundaries of a cocoa farm in Osun State needs to record the displacement of each corner from a reference point to accurately register the land title.
Sports and Athletics in Nigeria: Application: In events like the Eko Marathon or local inter-house sports, organizers specify the total distance of the race (e.g., 42 km). Athletes are concerned with covering this distance.
However, for a race that starts and ends at the same point (like a full lap on a track), an athlete's final displacement from the starting line is zero, even after running many kilometres. Coaches use these concepts to analyse athlete performance and strategize race tactics.
Example: A Super Eagles player on the football field covers a significant distance during a match, running all over the pitch.
However, their displacement from their starting position (e.g., center forward) to their final position on the pitch at any given moment might be small or even zero if they return to their original zone.