Position, Velocity, and Acceleration

AP Physics 1: Unit 1 Kinematics - Topic 1.1 Position, Velocity, and Acceleration

Learning Objectives

By the end of this lesson, students will be able to:

1. Define and differentiate between position, velocity, and acceleration.
2. Use kinematic equations to solve problems involving one-dimensional motion.
3. Interpret and create position vs. time, velocity vs. time, and acceleration vs. time graphs.
4. Apply concepts of kinematics to real-life scenarios.

Essential Knowledge

1. Position (x): The location of an object at a particular point in time, typically measured in meters (m).
2. Velocity (v): The rate at which an object's position changes over time, measured in meters per second (m/s). It includes both speed and direction.
3. Acceleration (a): The rate at which an object's velocity changes over time, measured in meters per second squared (m/s²).

Lesson Content

1. Position

• Definition: Position is a point in space where an object is located.
• Notation: Typically denoted as ????x for horizontal motion or ????y for vertical motion.
• Example: If a car is 50 meters east of a traffic light, its position is ????=50x=50 meters.

2. Velocity

• Definition: Velocity is the speed of an object in a specific direction.
• Formula: ????=Δ????Δ????v=ΔtΔx​
  • Δ????Δx is the change in position.
  • Δ????Δt is the change in time.
• Example: If a car travels 100 meters in 5 seconds, its velocity is ????=100 m5 s=20 m sv=5s100m​=20m s.

3. Acceleration

• Definition: Acceleration is the rate of change of velocity.
• Formula: ????=Δ????Δ????a=ΔtΔv​
  • Δ????Δv is the change in velocity.
  • Δ????Δt is the change in time.
• Example: If a car's velocity increases from 0 to 20 m/s in 5 seconds, its acceleration is ????=20 m s5 s=4 m s2a=5s20m s​=4m s2.

Visual Representations

1. Position vs. Time Graph

• Description: Shows how position changes over time.
• Interpretation: The slope of the graph represents velocity.Position vs. Time Graph

2. Velocity vs. Time Graph

• Description: Shows how velocity changes over time.
• Interpretation: The slope of the graph represents acceleration. The area under the graph represents displacement.Velocity vs. Time Graph

3. Acceleration vs. Time Graph

• Description: Shows how acceleration changes over time.
• Interpretation: The area under the graph represents the change in velocity.Acceleration vs. Time Graph

Real-Life Examples

1. Driving a Car:
   • Position: Your car is parked 10 meters from your house.
   • Velocity: You drive at a constant speed of 60 km/h (16.67 m/s).
   • Acceleration: You accelerate from 0 to 60 km/h in 10 seconds, giving an acceleration of 1.67 m s21.67m s2.
2. Free Fall:
   • Position: A ball is dropped from a height of 20 meters.
   • Velocity: The velocity increases as it falls due to gravity.
   • Acceleration: The acceleration is constant at 9.8 m s29.8m s2 (acceleration due to gravity).

Practice Problems

1. Problem 1:
   • A car travels 150 meters in 10 seconds. What is its average velocity?
   • Solution: ????=150 m10 s=15 m sv=10s150m​=15m s.
2. Problem 2:
   • A car accelerates from rest to 30 m/s in 5 seconds. What is its acceleration?
   • Solution: ????=30 m s5 s=6 m s2a=5s30m s​=6m s2.
3. Problem 3:
   • A ball is thrown upwards with an initial velocity of 20 m/s. How high does it go before it starts falling back down?
   • Solution: Using ????2=????2+2????????v2=u2+2as where ????=0 m sv=0m s, ????=20 m su=20m s, and ????=−9.8 m s2a=−9.8m s2: 0=(20)2+2(−9.8)????  ⟹  ????=40019.6≈20.4 m0=(20)2+2(−9.8)s⟹s=19.6400​≈20.4m

Summary

Understanding the concepts of position, velocity, and acceleration is fundamental in kinematics. By mastering these concepts and their graphical representations, students can analyze and predict the motion of objects in various contexts. Practice problems and real-life examples help solidify these concepts, making them more intuitive and applicable.