Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Define and differentiate between scalar and vector quantities.
• Distinguish between distance/displacement and speed/velocity.
• Calculate average speed and average velocity.
• Solve problems involving one-dimensional motion.
• Interpret simple displacement-time graphs.

Lesson summary

Welcome to the exciting world of Mechanics! This branch of physics deals with motion and the forces that cause it. Specifically, in Grade 10, we'll begin by examining motion in one dimension – think of a car driving straight down a road, a train on a track, or an object falling vertically. Understanding motion is crucial, not just for succeeding in Physical Sciences, but also for making sense of the world around you. Think about road safety, sports, engineering, and even predicting the weather. The concepts we learn this week form the foundation for understanding more complex topics like projectile motion, forces, and energy.

Lesson notes

2.1 Scalar vs.

Vector Quantities: Scalar Quantities: These have magnitude (size) only. They are described by a number and a unit.

Examples include: Distance:* The total length of the path travelled. For example, a car might travel a distance of 200 km.

Speed:* How fast an object is moving, regardless of direction. For example, a car's speed might be 100 km/h.

Time:* The duration of an event. For example, a journey might take 3 hours.

Mass:* The amount of "stuff" in an object. For example, a bag of sugar has a mass of 2.5 kg.

Vector Quantities: These have both magnitude and direction. They are described by a number, a unit, and a direction.

Examples include: Displacement:* The change in position of an object from its starting point. It is a straight-line distance with a specified direction. For example, a car might have a displacement of 150 km East.

Velocity: How fast an object is moving in a particular direction. For example, a car's velocity might be 80 km/h North.

Force:* A push or pull that can cause a change in motion. For example, a force of 50 N upwards.

Acceleration:* The rate of change of velocity. For example, an acceleration of 2 m/s² to the left. Important

Note: Direction can be indicated in various ways, such as using compass directions (North, South, East, West), left/right, up/down, positive/negative, or an angle relative to a reference point. 2.2 Distance vs.

Displacement: Imagine a taxi in Johannesburg driving from the Park Station to the Nelson Mandela Bridge. The taxi driver might take a circuitous route through the city streets.

Distance:* The total length of the road the taxi travels (e.g., 5 km).

Displacement: The straight-line distance from Park Station to the Nelson Mandela Bridge, including the direction (e.g., 1 km North-West).

Key Difference: Distance is a scalar quantity, while displacement is a vector quantity. 2.3 Speed vs.

Velocity: Consider a runner completing a 400m track race.

Average Speed:* The total distance covered divided by the total time taken.

Formula: `Average Speed = Total Distance / Total Time`

Example: If the runner completes the race in 50 seconds, their average speed is 400 m / 50 s = 8 m/s.

Average Velocity:* The change in displacement divided by the total time taken.

Formula: `Average Velocity = Change in Displacement / Total Time`

Example: If the runner starts and ends at the same point, their displacement is zero.

Therefore, their average velocity is 0 m/s, even though their average speed was 8 m/s.

Key Difference: Speed is a scalar quantity, while velocity is a vector quantity. Speed indicates how quickly something is moving, velocity indicates how quickly something is changing its position. 2.4 Calculating Average Speed and Average Velocity: Let's work through some examples: Example 1: A bus travels 120 km from Cape Town to Worcester in 2 hours.

Calculate: a) The average speed of the bus. b) The average velocity of the bus if Worcester is directly East of Cape Town.

Solution: a) Average Speed = Total Distance / Total Time = 120 km / 2 hours = 60 km/h b) Average Velocity = Change in Displacement / Total Time = 120 km East / 2 hours = 60 km/h East Example 2: A learner walks 50 m North, then 30 m South. The entire journey takes 40 seconds.

Calculate: a) The distance travelled. b) The magnitude of the displacement. c) The average speed. d) The magnitude of the average velocity.

Solution: a) Distance = 50 m + 30 m = 80 m b) Displacement = 50 m North - 30 m South = 20 m North (We treat North as positive and South as negative) Magnitude of displacement = 20m c) Average Speed = Total Distance / Total Time = 80 m / 40 s = 2 m/s d) Average Velocity = Change in Displacement / Total Time = 20 m North / 40 s = 0.5 m/s North Magnitude of average velocity = 0.5 m/s 2.5 Displacement-Time Graphs: These graphs show the displacement of an object over time. The slope of the graph represents the velocity. A steeper slope indicates a higher velocity. A horizontal line indicates that the object is stationary (velocity is zero). A straight line indicates constant velocity. A curved line indicates changing velocity (acceleration). A negative slope indicates movement in the opposite direction.

Example: Imagine a car moving away from a starting point, then stopping, then returning to the starting point. The displacement-time graph might look like this (description, not a drawn graph): From 0 to 5 seconds: A straight line sloping upwards (positive velocity, moving away).

From 5 to 10 seconds: A horizontal line (zero velocity, stopped).

From 10 to 15 seconds: A straight line sloping downwards (negative velocity, moving back). Guided Practice (With Solutions)

Question 1: A cyclist travels 5 km East and then 3 km West. The total trip takes 30 minutes. a) What is the total distance travelled? b) What is the magnitude of the cyclist's displacement? c) Calculate the cyclist's average speed in km/h. d) Calculate the magnitude of the cyclist's average velocity in km/h.