Overview
This lecture covers how to calculate velocity for objects accelerating at constant rates and explains acceleration and terminal velocity for objects falling through fluids.
Calculating Velocity at Constant Acceleration
- Acceleration (a) is calculated by dividing change in velocity by time: ( a = \frac{\Delta v}{t} ).
- For constant acceleration, use the formula: ( v^2 - u^2 = 2as ).
- ( v ) = final velocity, ( u ) = initial velocity, ( a ) = acceleration, ( s ) = distance.
- You do not need to memorize this formula for exams; it will be provided.
- Formula rearrangement allows solving for distance, acceleration, or final velocity depending on the problem.
Sample Calculations
- Example 1: With ( v = 12,m/s ), ( u = 8,m/s ), ( a = 2,m/s^2 ), ( s = 20,m ).
- Example 2: With ( u = 3,m/s ), ( v = 5,m/s ), ( s = 50,m ), found ( a = 0.16,m/s^2 ).
- Example 3: With ( u = 20,m/s ), ( a = 5,m/s^2 ), ( s = 50,m ), solved for ( v = 30,m/s ).
Acceleration and Terminal Velocity in Fluids
- Objects falling towards Earth accelerate at approximately ( 9.8,m/s^2 ) due to gravity.
- Air resistance (friction with air) acts upwards against falling objects.
- When air resistance balances gravity, the object stops accelerating and moves at constant speed: this is terminal velocity.
- Terminal velocity varies based on the object's shape and the friction it experiences in the fluid (air or liquid).
Key Terms & Definitions
- Acceleration — The rate at which velocity changes over time.
- Terminal Velocity — The constant speed reached when the force of air resistance balances the force of gravity.
- Air Resistance — The frictional force air exerts against a moving object.
- Gravity — The force that pulls objects toward Earth at ( 9.8,m/s^2 ).
Action Items / Next Steps
- Practice rearranging and using the ( v^2 - u^2 = 2as ) equation with different variables.
- Learn and understand the concept of terminal velocity.
- Review textbook or revision book acceleration exercises for additional practice.