Kinetic Curves Review Station
Station Task Placard MS-PS3-1 Energy Investigation
Kinetic Energy \( (KE = \frac{1}{2}mv^2) \)
Kinetic Curves: Mass vs. Speed
Analyze the two energy graphs below. Discover why changing speed alters kinetic energy far more drastically than changing mass.
Review Station
A
Mass vs. Kinetic Energy
Speed = 10 m/s (Constant)
0 500 1000 1500 2000 10 20 30 40 Mass (kg) Energy (J)
Mass Speed KE (J) Change
10 kg 10 m/s 500 J Baseline
20 kg (2×) 10 m/s 1000 J Doubles (2×)
Graph Rule: Direct & Linear
Straight line through (0,0). When mass doubles, kinetic energy doubles (2×).
B
Speed vs. Kinetic Energy
Mass = 10 kg (Constant)
0 2000 4000 6000 8000 10 20 30 40 Speed (m/s) Energy (J)
Speed Mass KE (J) Change
10 m/s 10 kg 500 J Baseline
20 m/s (2×) 10 kg 2000 J Quadruples (4×)
Graph Rule: Non-Linear & Quadratic
Upward curve getting steeper. When speed doubles, kinetic energy quadruples (4× = \(2^2\)).
Quick Comparison Matrix
| Comparison Feature | Graph A: Mass vs. KE | Graph B: Speed vs. KE |
|---|
| Graph Shape | Straight diagonal line | Curved parabola (gets steeper) |
| Mathematical Relationship | Direct / Proportional (\( KE \propto m \)) | Quadratic / Squared (\( KE \propto v^2 \)) |
| If Value Doubles (2×) | Kinetic energy doubles (2×) | Kinetic energy quadruples (4×) |
| If Value Triples (3×) | Kinetic energy triples (3×) | Kinetic energy increases by 9× (\(3^2\)) |
Station Instructions
1. Keep this placard visible at your station. 2. Turn to Page 2 (Student Recording Sheet). 3. Use the data and graphs above to complete Parts 1 through 4 with your team.
Page 1 of 2
Student Recording Sheet Kinetic Energy Review Station
Score: ______ / 20 pts
Name:
Date:
Period:
Group:
1 Part 1: Graph Anatomy Analysis
Refer to Graphs A & B on Page 1
- Describe the visual shape of each graph line and what it shows:
Graph A (Mass vs. KE) Shape:
Graph B (Speed vs. KE) Shape:
- On both graphs, what variable is on the X-axis (independent) vs. the Y-axis (dependent)?
2 Part 2: The Multiplier Challenge
Calculate the new Kinetic Energy
A cart starts with an initial Kinetic Energy of 100 Joules. Predict its new kinetic energy after each change:
| Initial State | Modification Made | Multiplier Rule | New Kinetic Energy (J) |
|---|
| Cart has 100 J | Mass is doubled (2× mass, same speed) | KE × 2 | |
| Cart has 100 J | Speed is doubled (2× speed, same mass) | KE × (2²) = KE × 4 | |
| Cart has 100 J | Mass is tripled (3× mass, same speed) | KE × 3 | |
| Cart has 100 J | Speed is tripled (3× speed, same mass) | KE × (3²) = KE × 9 | |
3 Part 3: Real-World Crash Test Analysis
Application to Highway Safety
Crash Test Scenario: A 1,000 kg test car traveling at 20 m/s has 200,000 J of kinetic energy. The safety lab conducts two separate test trials:
Trial 1: Double the Mass
Mass increases to 2,000 kg at 20 m/s.
Predicted KE:
Trial 2: Double the Speed
Speed increases to 40 m/s with 1,000 kg.
Predicted KE:
Why are speeding violations in school zones penalized more strictly than slightly overloaded vehicles? Connect to graph shapes:
4 Part 4: CER Scientific Rebuttal Challenge
Exit Check
Student Claim: "Doubling the mass of an object and doubling its speed will increase its energy by the exact same amount because you are multiplying by 2 in both cases."
Write a scientific rebuttal to disprove this claim. Include Evidence from the graphs and Reasoning using mathematical relationships:
Middle School Physical Science • NGSS MS-PS3-1 Graphical Displays of Kinetic Energy Page 2 of 2
