Physics · 9th Grade · Kinematics and Linear Motion · Weeks 1-9

Speed and Velocity

Defining and calculating average and instantaneous speed and velocity.

• Common Core State Standards
• HS-PS2-1
• CCSS.MATH.CONTENT.HSF.IF.B.6

About This Topic

Free fall is a specialized case of linear motion where the only force acting on an object is gravity. This topic introduces the constant acceleration of 9.8 m/s² (on Earth) and explores how mass does not affect the rate at which objects fall in a vacuum. This concept is a cornerstone of the HS-PS2-1 standard and provides a bridge to understanding universal gravitation. Students also examine the role of air resistance and how it leads to terminal velocity in real-world scenarios.

Historically, this topic allows for a discussion of Galileo's experiments and how they challenged Aristotelian views, mirroring the shift toward empirical evidence in science. This topic comes alive when students can physically model the patterns of falling objects and use technology to capture data that is otherwise too fast to see.

Key Questions

1. Differentiate between average speed and average velocity using a round trip example.
2. Explain how an object can have a high speed but zero average velocity.
3. Predict the instantaneous velocity of an object from a position-time graph.

Learning Objectives

• Calculate average speed and average velocity for an object undergoing linear motion.
• Differentiate between speed and velocity by analyzing displacement and distance traveled in various scenarios.
• Predict the instantaneous velocity of an object at a specific time using a position-time graph.
• Explain how an object can have a non-zero speed and a zero average velocity using a concrete example.

Before You Start

Introduction to Motion

Why: Students need a basic understanding of distance, displacement, and time intervals before calculating speed and velocity.

Scalar and Vector Quantities

Why: Understanding the difference between scalar (like distance, speed) and vector (like displacement, velocity) quantities is fundamental to this topic.

Key Vocabulary

Speed	A scalar quantity representing the rate at which an object covers distance. It does not consider direction.
Velocity	A vector quantity representing the rate at which an object changes its position. It includes both speed and direction.
Average Speed	The total distance traveled divided by the total time elapsed.
Average Velocity	The total displacement divided by the total time elapsed. Displacement is the change in position from the starting point.
Instantaneous Velocity	The velocity of an object at a specific moment in time, often determined from the slope of a position-time graph at that point.

Watch Out for These Misconceptions

Common Misconception

Heavier objects fall faster than lighter objects.

What to Teach Instead

In the absence of air resistance, all objects accelerate at the same rate. Hands-on 'vacuum chamber' demonstrations or dropping two different masses with low air resistance helps students see that gravity acts equally on all matter.

Common Misconception

Gravity stops acting on an object at the peak of its flight when it's thrown up.

What to Teach Instead

Gravity is a constant force. If it stopped, the object would never come back down. Structured discussion about the velocity being zero while acceleration remains -9.8 m/s² helps clarify this distinction.

Active Learning Ideas

Inquiry Circle: The Great Drop

Students drop pairs of objects with different masses but similar shapes (like a heavy ball and a light ball) from a height. They use slow-motion video on their phones to determine if they hit the ground at the same time.

30 min·Small Groups

Simulation Game: Terminal Velocity Design

Using coffee filters, students experiment with how surface area and mass affect the time it takes to reach the floor. They must design a 'parachute' that results in the slowest possible descent, modeling terminal velocity.

40 min·Small Groups

Think-Pair-Share: Gravity on Other Worlds

Students are given the gravitational acceleration for the Moon and Mars. They must calculate how much longer it would take a rock to fall 10 meters on those worlds compared to Earth and discuss the implications for astronauts.

20 min·Pairs

Real-World Connections

• Race car engineers at NASCAR use precise calculations of speed and velocity to optimize car performance and strategize during races, considering track conditions and competitor movements.
• Air traffic controllers monitor the speed and velocity of aircraft using radar systems to maintain safe separation distances and manage flight paths into busy airports like Hartsfield-Jackson Atlanta International Airport.
• Athletic coaches analyze the speed and velocity of their athletes during training and competition to identify areas for improvement in technique and performance, such as a sprinter's acceleration or a baseball pitcher's release velocity.

Assessment Ideas

Quick Check

Present students with a scenario: A student walks 5 meters east, then 5 meters west, taking 10 seconds total. Ask: 'What is the student's average speed? What is the student's average velocity? Explain your answers.'

Exit Ticket

Provide students with a simple position-time graph showing an object moving back and forth. Ask them to: 1. Identify the time interval when the object's speed was highest. 2. Calculate the object's average velocity over the entire trip.

Discussion Prompt

Pose the question: 'Can an object have a high speed but a zero average velocity? Describe a real-world situation where this occurs and explain why.'

Frequently Asked Questions

Why do all objects fall at the same rate regardless of mass?

While a heavier object has a greater gravitational force pulling it down, it also has more inertia, making it harder to move. These two effects perfectly cancel each other out. As a result, every object near Earth's surface experiences the same acceleration of 9.8 m/s² when air resistance is ignored.

What is terminal velocity and how is it reached?

Terminal velocity occurs when the upward force of air resistance equals the downward force of gravity. At this point, the net force is zero, and the object stops accelerating, continuing to fall at a constant speed. This is why skydivers don't keep getting faster forever.

Does gravity change depending on where you are on Earth?

Yes, slightly. Because Earth is not a perfect sphere and its density varies, gravity is slightly stronger at the poles than at the equator. However, for 9th-grade physics, we use the average value of 9.8 m/s² as a reliable constant for our calculations.

How can active learning help students understand free fall?

Active learning through video analysis allows students to 'freeze time.' By marking the position of a falling ball frame-by-frame, they can see the distance between positions increasing, which provides visual proof of acceleration. This evidence-based approach is much more convincing than simply being told a numerical value for 'g'.