Velocity and Acceleration
This section delves deeper into the concepts of velocity and acceleration.
Definition: Velocity is an object's speed in a given direction. It is a vector quantity.
Students should be able to explain the distinction between vector and scalar quantities as they apply to displacement, distance, velocity, and speed.
Example: An object moving in a circle has constant speed but changing velocity, as the direction is constantly changing.
The concept of acceleration is introduced:
Definition: Acceleration is the rate of change of velocity over time.
The equation for acceleration is:
a = Δv / t
where a is acceleration in meters per second squared (m/s²), Δv is change in velocity in meters per second (m/s), and t is time in seconds (s).
Highlight: An object that slows down is decelerating.
Students should be able to estimate the magnitude of everyday accelerations.
Velocity-Time Graphs and Further Calculations
This section covers the interpretation and use of velocity-time graphs.
The acceleration of an object can be calculated from the gradient of a velocity-time graph. The distance traveled (or displacement) can be calculated from the area under a velocity-time graph.
Students should be able to:
- Draw velocity-time graphs from measurements
- Interpret lines and slopes to determine acceleration
- Interpret enclosed areas in velocity-time graphs to determine distance traveled
- Measure the area under a velocity-time graph by counting squares when appropriate
An important equation for uniform acceleration is introduced:
v² - u² = 2as
where v is final velocity (m/s), u is initial velocity (m/s), a is acceleration (m/s²), and s is distance (m).
Highlight: Near Earth's surface, any object falling freely under gravity has an acceleration of about 9.8 m/s².
The concept of terminal velocity is briefly mentioned, where an object falling through a fluid eventually reaches a constant speed due to the balance of forces.
