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# Finding the Slope of a Velocity vs Time Graph

Lesson 9 of 11

## Objective: Students will determine the slopes of velocity vs time graphs.

*75 minutes*

This lesson focuses on the meaning behind the shape and slope of velocity vs time graphs. This lesson addresses the standards HSA-CED.A2 and HS-PS2-1 standards because it asks students to create a mathematical expression for graphical velocity vs time data. It also aligns with the NGSS Practices of Developing and Using Models (SP2) and Analyzing and Interpreting Data (SP4) for Science because students use logic to create explanations that demonstrate their understanding of the meaning of the slope and shape of a velocity vs time graph.

The concept of uniform acceleration is useful in constructing an explanation of concepts like free fall, projectile motion, and forces like weight and the normal force later on in the curriculum. This lesson on interpreting the slope of velocity vs time graphs follows lessons on connecting motion maps to position and velocity vs time graphs and interpreting the slope of position vs time graphs. Within this lesson, students obtain information for the meaning behind the slope and shape of velocity vs time graphs from a set of video notes with pause points. Students work in pairs to demonstrate their understanding using a velocity vs time worksheet inspired by the American Modeling Teaching Association. Finally, students work in teams using an online graphing tool to create a velocity vs time graph to model the motion of an object. I assess student understanding throughout the lesson using informal check-ins, and will assess each student's work at the end of the school day.

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#### Bell-ringer

*5 min*

At the beginning of each lesson, I have a quick Bell-ringer activity to get students focused on the tasks for today's lesson. There is a slide with the date, the objective and an additional prompt projected on the interactive whiteboard with a red label that says "COPY THIS" in the top left-hand corner. Sometimes the additional prompt is a BIG IDEA for the lesson or the Quote of the Day or a Quick Fact from current events that is related to the lesson. The red label helps my students easily interact with the information as soon as they enter the room and avoids losing transition time as students enter the classroom.

Today's additional prompt is the BIG IDEA that the slope of a velocity vs graph helps us calculate the acceleration of an object. I choose this BIG IDEA because I want students to recognize extend patterns within data.

#### Resources

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To start today's lesson, I include a set of notes in the form of an EDpuzzle that I project at the interactive whiteboard at the front of the room. This part of the lesson focuses on the calculating and interpreting the slope of a velocity vs time graph. For the first ten minutes, I play the EDpuzzle at the front of the room for the entire class and pause at the pause points that I embed as green question marks in the video.

During the first ten minutes, students take notes in their notebooks. I ask students if they have any questions or concerns about the methods discussed in the video. We have a whole class discussion for 2-4 minutes. Some students ask, "Why does he use both [FWD] and East?" and "How can you accelerate in a direction that is opposite to your motion?" Another student comments that "Finding the slope (of a graph)is really important in physics." During the last minute of this section of the lesson, I post this video on our class Edmodo wall so that students can watch, pause and replay the video outside of class. During the next section, students are given a set of modeling physics worksheets to complete.

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This section of the lesson gives students the opportunity to apply the information they learn using the EDpuzzle notes from the previous section on velocity vs time graphs. I distribute a set of handouts that student pairs work on individually for 25 minutes. Students analyze data and determine the acceleration of objects, predict how far the object travels and identify quantities from word problems that relate to velocity and time data for a scenario. While students work independently, I circulate and answer student questions. I also remind students to look at the online resources posted on our class website if they find any of the topics covered in the handout puzzling. After 25 minutes pass, I ask students to turn to their elbow partners and spend five minutes discussing any challenges they had while working on the assignment.

After 5 minutes pass, I ask students pairs to spend 10 minutes or so working together on the second handout using their new level of understanding. I circulate and ask groups to discuss their overall understanding of analyzing velocity vs time graphs. While I am circulating, I ask students who complete the activities quicker than other teams to work on Quick Checks from the extras bin at the front resource area. One student from each table grabs the quick checks for their table and students work on them individually while I circulate the room for ten more minutes. During the next section, students write down their perspectives explaining the meaning of the slope of a velocity vs time graph.

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#### Closure

*10 min*

I ask students to write a short summary of the most important part of today's lesson in their notebooks. Some student responses include, "Using [FWD] to represent a velocity moving to the right and using [BKWD] to represent moving to left." and "Showing that the slope of a velocity vs time graph is the same as the acceleration of an object." Click here to see an example of student work.

For homework, I ask students to go to this graphing calculator website and generate a velocity vs time graph. I ask that they describe a scenario that corresponds to their graphs.

#### Resources

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- LESSON 1: Lessons from Galileo
- LESSON 2: Investigating Basic Types of Physics Graphs
- LESSON 3: Motion in Terms of Position and Time
- LESSON 4: Introduction to Linear Motion
- LESSON 5: Modeling Motion Using Motion Maps And Position vs Time Graphs
- LESSON 6: Modeling Motion in Terms of Velocity vs Time Graphs, Part 1
- LESSON 7: Modeling Motion in Terms of Velocity vs Time Graphs, Part 2
- LESSON 8: Finding the Slope of a Position vs Time Graph
- LESSON 9: Finding the Slope of a Velocity vs Time Graph
- LESSON 10: Introducing Gravitational Field Strength
- LESSON 11: Galileo's Equations of Motion