MS-PS3-1: Graphing Kinetic Energy Against Mass and Speed
In plain English: MS-PS3-1 is the NGSS middle school performance expectation that asks students to construct and interpret graphs of data to describe how kinetic energy depends on an object's mass and, separately, on its speed. Doubling the mass doubles the kinetic energy, while doubling the speed makes it four times as large. It is usually taught in middle school physical science.
Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.
Clarification Statement: Emphasis is on descriptive relationships between kinetic energy and mass separately from kinetic energy and speed. Examples could include riding a bicycle at different speeds, rolling different sizes of rocks downhill, and getting hit by a wiffle ball versus a tennis ball.
Next Generation Science Standards · Disciplinary Core Idea: Energy · Official standard
Students build and read graphs of data to describe how the kinetic energy of an object depends on its mass and, separately, on its speed. Kinetic energy is the energy an object has because it is moving. Students graph kinetic energy against mass with the speed kept the same, and against speed with the mass kept the same, and then describe each graph in words: a straight line through zero for mass, and a curve that gets steeper and steeper for speed.
The NGSS Clarification Statement says: "Emphasis is on descriptive relationships between kinetic energy and mass separately from kinetic energy and speed. Examples could include riding a bicycle at different speeds, rolling different sizes of rocks downhill, and getting hit by a wiffle ball versus a tennis ball." This performance expectation has no Assessment Boundary. The page uses the formula kinetic energy = ½ × mass × speed², or KE = ½mv², only as a tool for filling in data tables and checking values; the goal is to describe the graphs. Energy is in joules (J), mass in kilograms (kg) and speed in meters per second (m/s). All data sets are invented for teaching and use realistic masses and speeds.
Learning Objectives
By the end of this lesson, students will be able to:
Construct a graph of kinetic energy against mass from data in which the speed stays the same
Construct a graph of kinetic energy against speed from data in which the mass stays the same
Describe each graph in words: kinetic energy is proportional to mass, and it grows with the square of speed
Use the graphs to predict kinetic energy and to explain everyday cases, such as why a faster bike or a heavier ball is harder to stop
Prior Knowledge Required
Students should already be comfortable with:
Using evidence to relate the speed of an object to its energy 4-PS3-1
Plotting points and drawing line graphs on a coordinate grid 5.G.A.2
Whole-number exponents, such as 3² = 3 × 3 = 9 6.EE.A.1
Measuring mass in kilograms and speed in meters per second
Hold up a wiffle ball (a light plastic ball with holes) and a tennis ball of about the same size. Do not throw them at anyone.
Warm-Up Prompt
"Imagine each ball rolls toward a row of empty paper cups at the same speed. Which one knocks the cups farther? Now imagine the same tennis ball rolling slowly, then fast. Which knocks the cups farther? Which do you think matters more, making the ball twice as heavy or making it twice as fast?"
Take a quick vote on the last question and record the result. Tell students the class will settle it with graphs, and write the term kinetic energy (energy of motion) on the board.
Direct Instruction15 minutes
Key words.Kinetic energy is the energy an object has because it is moving. It is measured in joules (J); lifting a small apple 1 meter takes about 1 J. Mass is the amount of matter in an object, in kilograms (kg). Speed is how far an object goes each second, in meters per second (m/s). Two quantities are proportional when doubling one doubles the other; their graph is a straight line through zero. A quantity squared is multiplied by itself: 4² = 4 × 4 = 16.
Scientists calculate kinetic energy with KE = ½ × m × v², where m is the mass and v is the speed. Use the formula to fill data tables, then let the graphs tell the story. To see the effect of one quantity, keep the other one the same: change only the mass, or only the speed.
Riding a bicycle at different speeds (speed changes, mass stays)
A rider and bike have a mass of 60 kg in all. The rider pedals at 2, 4, 6 and 8 m/s (invented data). Diagram 1 shows the graph.
Result: KE = ½ × 60 × v² gives 120, 480, 1,080 and 1,920 J. The graph is a curve that gets steeper. Doubling the speed from 2 to 4 m/s multiplies the kinetic energy by 4 (120 J to 480 J).
Rocks of different sizes rolling downhill (mass changes, speed stays)
Four rocks roll down the same grassy slope, and video shows each one moving at about 4.0 m/s at the bottom. Their masses are 0.5, 1.5, 3.0 and 6.0 kg (invented data). Diagram 2 shows the graph. Watch from the side of a slope like this, never from below it.
Result: KE = ½ × m × 4.0² = 8 × m gives 4, 12, 24 and 48 J. The graph is a straight line through zero: the 6.0 kg rock has twice the mass of the 3.0 kg rock and twice the energy.
A wiffle ball versus a tennis ball (same speed, different mass)
A wiffle ball (about 0.020 kg) and a tennis ball (about 0.058 kg) both move at 10 m/s.
Result: Wiffle ball: ½ × 0.020 × 10² = 1.0 J. Tennis ball: ½ × 0.058 × 10² = 2.9 J. At the same speed, the tennis ball has 2.9 times the mass and 2.9 times the kinetic energy, which is why it stings more and why a game of catch with a tennis ball needs more care.
Which matters more: mass or speed?
Start with the 60 kg bike and rider at 4 m/s (480 J). Compare doubling the mass (a 120 kg tandem bike with two riders, still at 4 m/s) with doubling the speed (the 60 kg bike at 8 m/s).
Result: Double the mass: ½ × 120 × 4² = 960 J, two times as much. Double the speed: ½ × 60 × 8² = 1,920 J, four times as much. Doubling the speed changes kinetic energy more than doubling the mass.
Reading a graph backward
Use the curve in Diagram 1. At what speed does the 60 kg bike and rider have 750 J of kinetic energy?
Result: Move across from 750 J on the vertical axis to the curve, then down to the speed axis: about 5 m/s. Check: ½ × 60 × 5² = 30 × 25 = 750 J.
After each example, ask: "What stayed the same? What changed? What shape is the graph, and what does the shape say in words?"
Guided Practice15 minutes
Pairs use the invented data below for a 0.20 kg toy car released from different heights on a ramp. A phone video gave its speed at the bottom. Pairs complete the table, build the graph and describe it.
Guided practice data (invented): 0.20 kg toy car
Trial
Speed v (m/s)
v² (m²/s²)
KE = ½ × 0.20 × v² (J)
1
0.5
0.25
2
1.0
1.00
3
1.5
2.25
4
2.0
4.00
5
2.5
6.25
Fill in the last column. (Since ½ × 0.20 = 0.10, multiply each v² by 0.10.)
Plot kinetic energy (vertical axis) against speed (horizontal axis) and connect the points with a smooth curve. Label both axes with units.
Compare trials 2 and 4: the speed doubled. By what factor did the kinetic energy change?
Write one sentence that describes the shape of the graph and one sentence that says what it means.
Independent Practice10-15 minutes
Each student works with a second invented data set: a lab cart moving at 1.5 m/s each time, loaded so that its mass is 0.40, 0.80, 1.20 and 1.60 kg. Students compute the kinetic energy for each mass, draw a graph of kinetic energy against mass, and write a paragraph that compares the shape of this graph with the guided practice graph. The paragraph must name what stayed the same in each data set.
Independent practice data (invented): lab cart at 1.5 m/s
Trial
Mass m (kg)
Speed v (m/s)
KE (J)
1
0.40
1.5
2
0.80
1.5
3
1.20
1.5
4
1.60
1.5
Closure5 minutes
Return to the warm-up vote: "Which matters more, twice as heavy or twice as fast?" Students answer on a sticky note using one of today's graphs as evidence, then sketch the two graph shapes side by side and label each one "mass" or "speed."
Differentiation Strategies
For Struggling Students
Provide graph paper with the axes already drawn and scaled, so students focus on plotting and describing
Give a word bank for describing graphs: straight line, through zero, curve, gets steeper, doubles, four times
Fill in the first two rows of each kinetic energy table together before students finish the rest
For Advanced Students
Ask students to graph kinetic energy against speed squared (v²) for the guided practice data and explain why that graph is a straight line
Have students find two objects with the same kinetic energy but different masses and speeds, and mark both on one graph
Ask students to explain, using the speed graph, why stopping distances for cars grow quickly as speed goes up
Assessment Guidance
What to Look For
Check that students keep one quantity fixed when they describe the effect of the other, and that their graphs have labeled axes with units. Look for students who draw a straight line through the kinetic energy and speed data: ask them to compare the steps between points. Listen for clear descriptions: "doubling the mass doubles the kinetic energy" and "doubling the speed makes it four times as large." Students who square the mass instead of the speed, or forget the ½, need one more worked row with you.
02
Classroom Activities
3 Activities
1
Ramp and Cup Lab: Mass, Then Speed
25 minGroups of 3-4
Groups release a toy car down a ramp into a paper cup lying on its side with a doorway cut in the rim. The car pushes the cup along the floor, and the distance the cup slides shows how much energy the car had to give. In Part A the release height (and so the speed) stays the same while the mass changes; in Part B the mass stays the same while the speed changes.
Procedure
Part A (mass): release the car from the same mark each time. Tape 0, 2, 4 or 6 washers to it and record the total mass from a balance. Measure how far the cup slides, 3 trials each.
Part B (speed): use the car with 2 washers (0.10 kg) and release it from four different heights. Time the car over the last 0.50 m of the floor with phone video and compute its speed (distance ÷ time). Measure the cup slide, 3 trials each.
Graph the average slide distance against mass (Part A) and against speed (Part B).
Safety: keep the floor path clear, and stand to the side of the ramp.
Sample Data (invented)
Part A, same release mark: mass 0.05, 0.10, 0.15 and 0.20 kg gave average slides of 8, 15, 24 and 31 cm. Part B, 0.10 kg car: speeds of 0.6, 0.9, 1.2 and 1.5 m/s gave average slides of 5, 11, 20 and 31 cm.
Discussion Questions
In Part A, the 0.20 kg car has 4 times the mass of the 0.05 kg car. About how many times farther did its cup slide? What graph shape does that suggest?
In Part B, the speed went from 0.6 m/s to 1.2 m/s, which is double. Did the slide distance double, or did it grow by more? Which part of your graph shows this?
The slide distance is a stand-in for kinetic energy. What could make it an imperfect measure?
Modification for Distance Learning
Students use a toy car, a book ramp and a sock or paper cup at home, or they graph the sample data in a spreadsheet and post both graphs with a two-sentence description of each.
2
Wiffle Ball and Tennis Ball Drop
20 minGroups of 3
Instead of being hit by the balls, students let a wiffle ball and a tennis ball of about the same size fall into a tray of flour or sand and compare the craters. Dropping each ball from two heights gives two speeds, so the design separates the effect of mass from the effect of speed.
Procedure
Weigh both balls on a balance. Smooth the flour or sand flat before every drop.
Drop each ball from 0.50 m and from 1.00 m above the surface, 3 times each. Measure the depth of each crater with a ruler.
Phone video shows that both balls reach about 3.1 m/s after falling 0.50 m and about 4.4 m/s after 1.00 m; air slows the wiffle ball a little.
Compute the kinetic energy of each ball just before it lands and make a bar graph of kinetic energy and of crater depth for all four cases.
Safety: wear goggles, drop the balls gently straight down, and keep flour away from faces.
Sample Data (invented)
Wiffle ball 0.020 kg; tennis ball 0.058 kg. Kinetic energy at landing: wiffle ball 0.10 J (0.50 m) and 0.19 J (1.00 m); tennis ball 0.28 J (0.50 m) and 0.56 J (1.00 m). Average crater depth: wiffle ball 0.4 cm and 0.6 cm; tennis ball 0.9 cm and 1.4 cm.
Discussion Questions
Compare the two balls dropped from the same height. Which quantity is the same, which is different, and how do their kinetic energies compare?
The tennis ball dropped from 1.00 m has about twice the kinetic energy of the tennis ball dropped from 0.50 m. Its speed is only about 1.4 times as large. How does that fit the speed graph from class?
Use your bar graph to explain why players use a wiffle ball for backyard games.
Challenge Variation
Groups predict, then test, the drop height at which the wiffle ball makes a crater as deep as the tennis ball's crater from 0.50 m, and explain the prediction with kinetic energy.
3
Graph Match Card Sort
15 minPairs
Pairs get 12 cards: 4 data tables, 4 graph sketches and 4 descriptions in words. They match each table to its graph and its description, then write which quantity stayed the same in each set.
Card Set (invented data)
Table 1: a 2.0 kg ball at 1, 2, 3, 4 m/s; KE = 1, 4, 9, 16 J.
Table 2: balls at 2.0 m/s with masses 1, 2, 3, 4 kg; KE = 2, 4, 6, 8 J.
Table 3: a 40 kg skater at 2, 3, 4, 5 m/s; KE = 80, 180, 320, 500 J.
Table 4: carts at 3.0 m/s with masses 0.5, 1.0, 1.5, 2.0 kg; KE = 2.25, 4.5, 6.75, 9 J.
Graph cards: two straight lines through zero (one steep, one shallow) and two upward curves (one steep, one shallow).
Description cards: "Double the mass, double the energy" (two cards) and "Double the speed, four times the energy" (two cards).
Discussion Questions
Tables 2 and 4 both make straight lines. Which line is steeper, and why?
How can you tell a speed table from a mass table without reading the column headings?
Write a fifth table that would match a straight-line graph, and trade it with another pair.
Modification for Distance Learning
Post the cards as images on a shared slide; pairs drag them into matching rows during a video call.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Kinetic Energy of a Bicycle and Rider Against Speed
Invented data for a 60 kg bicycle and rider, drawn to scale. The mass stays the same and only the speed changes. The points lie on a curve that gets steeper: each extra 2 m/s adds more kinetic energy than the step before.
Diagram 2: Kinetic Energy of Rolling Rocks Against Mass
Invented data for four rocks, each moving at 4.0 m/s at the bottom of the same slope, drawn to scale. The speed stays the same and only the mass changes. The points lie on a straight line through zero, so kinetic energy is proportional to mass.
04
Homework Assignment
~30 min
MS-PS3-1 Homework: Graphing Kinetic Energy
Directions: All data sets are invented for practice. Use KE = ½ × m × v² where you need to fill in a table. Label every graph axis with a name and a unit, and describe each graph in words.
Part 1: Construct the Graphs (Problems 1-3)
A student and her kick scooter have a mass of 50 kg in all. She rides at 1, 2, 3, 4 and 5 m/s. (a) Compute the kinetic energy at each speed. (b) Graph kinetic energy against speed. (c) Describe the shape of the graph. (d) Use the pattern to predict the kinetic energy at 6 m/s.
A shopping cart rolls at 2.0 m/s with loads that make its total mass 15, 30, 45 and 60 kg. (a) Compute the kinetic energy for each mass. (b) Graph kinetic energy against mass. (c) Describe the graph in words, and say what stays the same in this data set.
On one set of axes, a student plans to draw two lines of kinetic energy against mass: one for objects moving at 0.5 m/s and one for objects moving at 1.0 m/s, with masses from 0 to 6 kg. (a) Compute the kinetic energy at 6 kg for each speed. (b) Which line is steeper, and by how many times? (c) Explain why.
Part 2: Interpret and Apply (Problems 4-6)
A student records three trials with a ball: Trial A, 0.5 kg at 2 m/s; Trial B, 1.0 kg at 2 m/s; Trial C, 1.0 kg at 4 m/s. She writes, "From Trial A to Trial C, the energy went up 8 times, so doubling the mass makes the energy 8 times as large." (a) Compute the kinetic energy for each trial. (b) Explain what is wrong with her conclusion. (c) Which two trials show the effect of mass alone, and which two show the effect of speed alone?
A baseball (0.145 kg) and a wiffle ball (0.020 kg) are each thrown at 12 m/s. (a) Compute the kinetic energy of each. (b) How many times as much kinetic energy does the baseball have? (c) Use your answer to explain why baseball players wear helmets but backyard wiffle ball players do not.
A 0.30 kg remote-control car drives at different speeds. (a) Use KE = ½ × 0.30 × v² to make a table for speeds 0, 1, 2, 3 and 4 m/s, and graph kinetic energy against speed. (b) From your graph, estimate the speed at which the car has 1.35 J. (c) Check your estimate with the formula.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Data Tables
Every kinetic energy value is correct, with units
One or two calculation or unit errors
Graph Construction
Axes labeled with names and units, sensible scale, points plotted correctly, correct shape (line or curve)
Missing a label or a unit, or points joined with the wrong shape
Describing Relationships
States that kinetic energy is proportional to mass and grows with the square of speed, and names what stayed the same
Says "more mass or more speed means more energy" without the pattern
Applying the Graphs
Uses the graphs to predict values and explain the everyday case
Prediction or explanation is incomplete
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All data sets are invented for practice. Use KE = ½ × m × v² where a calculation is needed, with mass in kg, speed in m/s and energy in joules (J). Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which of these objects has kinetic energy?
Answer: B
Kinetic energy is energy of motion, and only the rolling ball is moving. The book (choice A), the stretched band (choice C) and the battery (choice D) store energy, but none of them is moving.
Question 2 of 20 · Multiple Choice
Two balls roll at the same speed. Ball X has a mass of 2 kg and ball Y has a mass of 1 kg. How does the kinetic energy of ball X compare with ball Y?
Answer: C
At the same speed, kinetic energy is proportional to mass, so twice the mass gives twice the kinetic energy. Choice A squares the mass instead of the speed. Choice B reverses the comparison, and choice D ignores the mass.
Question 3 of 20 · Multiple Choice
A runner keeps the same mass but doubles her speed. What happens to her kinetic energy?
Answer: D
Kinetic energy grows with the square of speed: (2)² = 4, so doubling the speed makes it four times as large. Choice B treats speed like mass, as if the relationship were proportional. Choices A and C ignore or reverse the effect of speed.
Question 4 of 20 · Multiple Choice
A graph shows kinetic energy against mass for objects that all move at the same speed. What shape should it have?
Answer: B
With the speed fixed, kinetic energy is proportional to mass, which makes a straight line through zero. Choice C is the shape of the kinetic energy against speed graph. Choice D would mean mass has no effect, and choice A would mean extra mass adds less and less energy.
Question 5 of 20 · Multiple Choice
A graph shows kinetic energy against speed for one object. What shape should it have?
Answer: A
Kinetic energy grows with the square of speed, so each equal step in speed adds more energy than the last: the curve gets steeper. Choice B would mean doubling the speed only doubles the energy. Choice C forgets that speed changes the energy. Choice D would mean faster objects have less energy.
Question 6 of 20 · Multiple Choice
What is the kinetic energy of a 0.50 kg ball moving at 6.0 m/s?
Answer: C
KE = ½ × 0.50 × 6.0² = 0.25 × 36 = 9.0 J. Choice A forgets the ½ (0.50 × 36). Choice B multiplies mass by speed (0.50 × 6.0) without squaring. Choice D takes ½ × 0.50 × 6.0, again without squaring the speed.
Question 7 of 20 · Multiple Choice
A graph shows that a 70 kg runner has 560 J of kinetic energy at 4 m/s. At what speed would the runner have 2,240 J, which is 4 times as much?
Answer: B
Four times the kinetic energy needs twice the speed, because 2² = 4: 2 × 4 = 8 m/s. Check: ½ × 70 × 8² = 2,240 J. Choice A multiplies the speed by 4, as if kinetic energy were proportional to speed. Choice D multiplies the speed by about 1.41, which would only double the energy. Choice C gives ½ × 70 × 36 = 1,260 J.
Question 8 of 20 · Multiple Choice
A student wants to see how mass alone affects kinetic energy. Which pair of trials should she compare?
Answer: C
Only choice C keeps the speed the same (3 m/s) while the mass changes, so any change in kinetic energy comes from the mass. Choice B keeps the mass the same, so it shows the effect of speed. Choices A and D change both at once.
Question 9 of 20 · Multiple Choice
A soccer ball (0.43 kg) and a beach ball (0.10 kg) are kicked at the same speed. Which statement is correct?
Answer: C
At the same speed, more mass means more kinetic energy: the soccer ball has 4.3 times the mass and so 4.3 times the kinetic energy. Choice A and choice D use size instead of mass. Choice B forgets that mass matters too.
Question 10 of 20 · Multiple Choice
A loaded truck and a small car travel side by side at the same speed. Why does the truck have more kinetic energy?
Answer: A
At the same speed, kinetic energy is proportional to mass, and the loaded truck has much more mass. Choice B and choice D describe the truck, but height and sound do not set kinetic energy. Choice C is a result of the truck having more kinetic energy, not the cause.
Question 11 of 20 · Multiple Choice
A skater triples her speed while her mass stays the same. By what factor does her kinetic energy change?
Answer: A
Kinetic energy grows with the square of speed: 3² = 9. Choice B treats speed as if kinetic energy were proportional to it. Choice C doubles the factor of 3 instead of squaring it. Choice D takes half of 3, a mix-up with the ½ in the formula.
Question 12 of 20 · Multiple Choice
Invented data for objects all moving at the same speed: 1 kg has 6 J, 2 kg has 12 J and 3 kg has 18 J. If the pattern continues, how much kinetic energy does a 5 kg object have?
Answer: D
The data are proportional: 6 J for every kilogram, so 5 kg has 5 × 6 = 30 J. Choice A adds only one more 6 J step after 18 J. Choice C squares the mass (6 × 5²), and choice B doubles 24 J.
Question 13 of 20 · Multiple Choice
A 50 kg cyclist rides at 4 m/s. Which change gives her the largest increase in kinetic energy?
Answer: B
Doubling the mass multiplies the kinetic energy by 2. A speed 50% higher (6 m/s) multiplies it by 1.5² = 2.25, which is more. Choice C multiplies it by 1.25, and choice D by 1.25² ≈ 1.56. A modest rise in speed can matter more than a large rise in mass.
Question 14 of 20 · Multiple Choice
A graph of kinetic energy against speed shows two curves: one for a 1 kg ball and one for a 3 kg ball. Which description is correct?
Answer: D
At any one speed, kinetic energy is proportional to mass, so the 3 kg ball has 3 times the kinetic energy of the 1 kg ball and its curve is 3 times as high. Choice A and choice C ignore the mass. Choice B reverses the order of the curves.
Question 15 of 20 · Short Answer
Invented data for a 4.0 kg cart: at 1, 2, 3 and 4 m/s, its kinetic energy is 2, 8, 18 and 32 J. Describe the graph of kinetic energy against speed and the relationship it shows.
The points form a curve that starts at zero and gets steeper, not a straight line: the steps between points grow (6, 10, 14 J). Kinetic energy grows with the square of the speed: doubling the speed from 1 to 2 m/s, or from 2 to 4 m/s, makes the kinetic energy 4 times as large. The mass stayed the same, so the change comes from speed alone.
Question 16 of 20 · Short Answer
A 1,200 kg car travels at 10 m/s, then at 20 m/s. Compute its kinetic energy at each speed and explain what doubling the speed did.
At 10 m/s: ½ × 1,200 × 10² = 60,000 J. At 20 m/s: ½ × 1,200 × 20² = 240,000 J. Doubling the speed made the kinetic energy 4 times as large, so the brakes must remove four times as much energy to stop the car.
Question 17 of 20 · Short Answer
Two rocks roll down a hillside, each moving at 3.0 m/s. One has a mass of 4.0 kg and the other 12 kg. Compute each kinetic energy, and explain which rock would be more dangerous to stand in front of.
4.0 kg rock: ½ × 4.0 × 3.0² = 18 J. 12 kg rock: ½ × 12 × 3.0² = 54 J. At the same speed the 12 kg rock has 3 times the mass and 3 times the kinetic energy, so it would do more damage and is more dangerous. Never stand below a slope where rocks can roll.
Question 18 of 20 · Short Answer
A student plots kinetic energy against speed for one object and connects the points with a straight line through zero. Explain why this graph is not correct and how to tell from the data.
Kinetic energy is not proportional to speed: it grows with the speed squared, so the points lie on a curve that gets steeper. In the data, equal steps in speed give larger and larger steps in energy, and doubling the speed gives 4 times the energy, not 2 times. A straight line through zero would fit only if doubling the speed doubled the energy.
Question 19 of 20 · Short Answer
Plan an investigation to show how kinetic energy depends on speed alone. You have one basketball, an empty cardboard box on a gym floor, a meter stick, masking tape and a stopwatch. Say what you will change, what you will keep the same, what you will measure, and what graph you expect.
Change: how fast the basketball is rolled into the box (gentle, medium, hard). Keep the same: the ball (so the mass stays the same), the box, its starting spot and the floor. Measure: the ball's speed, by timing it over a taped 2 m stretch just before the box (speed = 2 m ÷ time), and how far the box slides as a sign of energy, with several trials at each speed. Graph: box slide (or computed kinetic energy) against speed, expected to be a curve that gets steeper.
Question 20 of 20 · Short Answer
A car near a school slows from 14 m/s to 10 m/s. Use the relationship between kinetic energy and speed to explain why this makes a large difference to safety.
Kinetic energy depends on the square of the speed. The ratio of speeds is 14 ÷ 10 = 1.4, so the car at 14 m/s has 1.4² = 1.96, almost 2 times the kinetic energy it has at 10 m/s. Slowing down by less than a third removes about half of the kinetic energy, so the car is much easier to stop and does far less harm in a collision.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does MS-PS3-1 mean?
MS-PS3-1 asks middle school students to build and read graphs of data that show how the kinetic energy of an object depends on its mass and on its speed, one at a time. The code stands for Middle School, Physical Science, core idea 3 (Energy), performance expectation 1.
Do students need the kinetic energy formula for MS-PS3-1?
The emphasis is on describing the relationships in words, from graphs: kinetic energy is proportional to mass and grows with the square of speed. Many teachers use KE = ½mv² to fill in data tables, as this page does, but the target is reading and building the graphs. MS-PS3-1 has no Assessment Boundary.
What is kinetic energy in simple terms?
Kinetic energy is the energy an object has because it is moving. A moving object can push things, dent things or speed other things up, and the more kinetic energy it has, the more it can do. A still object has no kinetic energy.
Why does speed affect kinetic energy more than mass?
Because kinetic energy depends on the speed squared. Doubling the mass doubles the kinetic energy, but doubling the speed multiplies it by 2 × 2 = 4. On a graph, mass gives a straight line and speed gives a curve that gets steeper.
What does a graph of kinetic energy against mass look like?
When the speed is kept the same, it is a straight line through zero: every extra kilogram adds the same amount of energy. A faster set of objects gives a steeper line, because each kilogram carries more energy at a higher speed.
Why must one variable stay the same in MS-PS3-1 data?
The Clarification Statement asks for the relationship with mass separately from the relationship with speed. If both change between two trials, you cannot tell which one caused the change in energy. So mass data are collected at one speed, and speed data with one mass.
How can you measure kinetic energy in a middle school lab?
Measure mass with a balance and speed with a stopwatch or phone video over a marked distance, then compute the kinetic energy. You can also use a sign of energy: how far a moving car pushes a paper cup, or how deep a dropped ball dents a tray of flour or sand. These stand-ins rise and fall with kinetic energy, though not perfectly.
How do the official examples fit MS-PS3-1?
Riding a bicycle at different speeds shows the speed relationship with the mass fixed. Rocks of different sizes rolling downhill at about the same speed show the mass relationship. A wiffle ball and a tennis ball moving at the same speed show that the heavier ball carries more energy, which is why it stings more.
What grade is MS-PS3-1 taught in?
NGSS sets middle school standards for grades 6-8 as a band, so it depends on the school. It is often part of an energy unit in grade 7 or 8 physical science. Students need to plot points and read graphs, and squaring a number helps for the speed relationship.
What comes after MS-PS3-1?
MS-PS3-5 asks students to argue that when an object's kinetic energy changes, energy is transferred to or from it. In high school, HS-PS3-1 uses kinetic energy in computational models of whole systems, and HS-PS3-2 models energy as motion of particles or energy stored in fields.
07
Related Standards
5 standards
These standards connect to MS-PS3-1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
4-PS3-1Prerequisite
Use evidence to explain how the speed of an object relates to its energy
Lesson coming soon
Alongside
MS-PS3-5Parallel
Argue that when kinetic energy changes, energy is transferred to or from the object
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