Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Define and differentiate displacement, velocity, and acceleration.
• Apply equations of motion to solve problems.
• Interpret graphs of motion.
• Solve problems involving relative velocity.
• Explain the significance of sign conventions.

Lesson summary

This week, we delve deeper into the fascinating world of mechanics, specifically focusing on motion in one dimension. Understanding how objects move along a straight line is crucial for comprehending more complex motions in two and three dimensions. This forms the foundation for understanding concepts like projectile motion, forces, and energy, which are essential for many careers in science, engineering, and technology. Understanding motion is not just an academic exercise; it helps us analyze everything from the speed of a taxi on the N1 to the trajectory of a soccer ball during a game. It empowers us to predict and control movement around us.

Lesson notes

2.1 Displacement, Velocity, and Acceleration These are the fundamental quantities describing motion. Displacement (Δx): The change in position of an object. It's a vector quantity, meaning it has both magnitude and direction. In one dimension, direction is indicated by a positive or negative sign. The SI unit for displacement is meters (m).

Example: A taxi travels from Johannesburg to Pretoria, a displacement of +55 km (assuming the direction from Johannesburg to Pretoria is positive). If it then returns to Johannesburg, the displacement is -55 km. The total displacement for the round trip is 0 km.

Velocity (v): The rate of change of displacement. It's also a vector quantity. The SI unit for velocity is meters per second (m/s). We distinguish between average velocity and instantaneous velocity.

Average velocity (v avg ):* The total displacement divided by the total time taken. v avg = Δx / Δt Instantaneous velocity:* The velocity at a specific instant in time. This is what your car's speedometer shows.

Acceleration (a): The rate of change of velocity. It's a vector quantity. The SI unit for acceleration is meters per second squared (m/s 2 ). Like velocity, we can have average acceleration and instantaneous acceleration.

Average acceleration (a avg ):* The change in velocity divided by the time taken. a avg = Δv / Δt A positive acceleration means the velocity is increasing in the positive direction or decreasing in the negative direction. A negative acceleration means the velocity is decreasing in the positive direction or increasing in the negative direction (often called deceleration). 2.2 Equations of Motion (Kinematic Equations) These equations relate displacement, velocity, acceleration, and time for motion with constant acceleration in one dimension. v = u + at (Final velocity = Initial velocity + (acceleration * time)) Δx = ut + (1/2)at 2 (Displacement = (Initial velocity time) + (1/2 acceleration * time 2 )) v 2 = u 2 + 2aΔx (Final velocity 2 = Initial velocity 2 + (2 acceleration Displacement)) Δx = (v + u)t/2 (Displacement = (Final velocity + Initial velocity)time/2)

Where: u = initial velocity v = final velocity a = constant acceleration Δx = displacement t = time Important Considerations: Choose a positive direction. All vector quantities (displacement, velocity, acceleration) must be assigned a sign (+ or -) based on this choice. Ensure all units are consistent (e.g., meters, seconds). These equations ONLY apply when the acceleration is CONSTANT.