Crash Course Slides Police Line Do Not Cross • Evidence Scene
CRASH COURSE
Unit 01: Forensic Physics Foundations
Forensic Reconstruction Unit
Confidential
The Witness Statement
"I was driving home. The light was green. I was going exactly 35 mph, the speed limit. Suddenly, that truck came out of nowhere and hit me. They must have been speeding!"
— Driver A (Sedan)
The Problem:
Both drivers claim the other was speeding. The only things left at the scene are:
Bent metal & shattered glass
Tire marks on the asphalt
Final resting positions of the cars
How do we find the truth?
Working Backwards
1. Final Position
Where did they stop?
2. The Impact
Energy & Momentum Transfer
3. Initial Speeds
The Truth
In Physics, we often find final velocity from initial. In Forensics, we do the reverse .
The Conservation Law
p = mv
Momentum = Mass × Velocity
In a closed system (like a collision), the total momentum before the crash must equal the total momentum after.
\[ \sum p_{initial} = \sum p_{final} \]
Why does this help?
We can determine vehicle masses from manufacturer data.
We can measure post-impact speeds from skid distances.
The only unknown? The speed before the crash.
Real-World Evidence
IMG_0234
Deformation Analysis
Crush depth tells us about energy lost to plastic deformation.
MEAS_44
Skid Mark Length
The length of the slide tells us how much kinetic energy was lost to friction.
LOG_88
Vehicle Specs
Standardized mass (curb weight) + weight of passengers and cargo.
Your Task: Become the investigator.
Case Briefing Teacher Guide Case Briefing Guide
Lesson 01: Forensic Physics Foundations
Teacher Resource
ID: FOR-TS-001
Objective
Students will understand the methodology of accident reconstruction by identifying how conservation of momentum allows investigators to determine pre-collision speeds from post-collision evidence.
Key Concepts
Conservation of Momentum: Total initial momentum equals total final momentum.Forensic Directionality: Working backwards from known final states to unknown initial states.Evidence Categories: Mass (vehicle specs), Final Velocity (skid analysis), Momentum Transfer (impact).
Time Allotment
50 Minutes
Materials Needed
Crash Course Slides
Case File Alpha Worksheet
Scientific Calculators
Instructional Sequence
1
The Hook: Witness Bias (10 min)
Start with the "Witness Statement" slide. Ask students: "Why can't we just believe Driver A or Driver B?"
Discussion Prompt: Human memory in high-stress situations is notoriously unreliable. Physics is the "impartial witness." We don't care what they said; we care what the asphalt shows.
2
The Physics of the Reverse (15 min)
Explain the Working Backwards concept. In standard physics problems, we are given "v initial" and asked for "v final." In reconstruction, we have the "result" and need the "cause."
Crucial Formula Note:
\( m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f} \)
Emphasize that if the cars stick together (inelastic), the right side simplifies to \( (m_1 + m_2)v_f \).
3
Independent Activity: Case File Alpha (20 min)
Students identify variables in a simplified crash scenario. They are not doing full calculations yet, but rather "mapping" the evidence.
4
Closing: The Road Ahead (5 min)
Preview the next lesson. Ask: "If we have the skid marks after the crash, how do we actually find the speed at the moment of impact?" This sets up Lesson 02: Friction.
Common Misconceptions
Energy vs. Momentum: Students often think energy is conserved in crashes. Remind them that kinetic energy is lost to heat/sound/metal deformation. Only momentum is truly conserved. System Boundaries: Ensure they understand the "system" includes both vehicles.
Extensions
For advanced students: Introduce the concept of Impulse (\(F \Delta t = \Delta p\)) and ask how crumple zones in cars increase the collision time to decrease force.
Incident Report Worksheet Evidence Dossier
CASE FILE: ALPHA-7
Incident #8821-XP | Location: 5th & Main St.
Investigating Officer
Incident Summary
On January 12th, at 14:30 hours, a 2022 Mid-Size Sedan (Vehicle 1) traveling North collided with a 2020 Compact SUV (Vehicle 2) that was stationary at a red light. Upon impact, the two vehicles became entangled (locked bumpers) and slid together as a single mass before coming to a stop 12 meters from the point of impact.
Part 1: Evidence Mapping
Before we can calculate, we must identify our knowns. Use the incident summary above to fill in the table.
Variable Value / Description Physics Symbol Mass of Vehicle 1 1,500 kg m1 Mass of Vehicle 2 m2 Initial Velocity of V2 v2i Post-Impact State —
Part 2: The Momentum Equation
Based on the fact that the cars entangled , write out the specific conservation of momentum equation for this system below.
1. In this specific case, which of the variables do we currently NOT know?
2. To find the initial speed of Vehicle 1, what piece of "missing evidence" do we need to calculate first? (Hint: Think about what happens right after they hit).
Part 3: Scene Sketch
Draw a simplified vector diagram of the moment immediately after the collision. Label the system's mass and the direction of the final velocity vector.
Sketch Area [720px x 400px]
Investigator Reflection
If Vehicle 1 had been a heavy freight truck instead of a sedan, but hit at the same speed, what would happen to the final distance they slid? Use physics terminology (momentum, mass) to explain.
Tire Tracks Slides SKID MARKS
Physics of Tire-Road Friction
SESSION 02: FRICTION & ENERGY
The Missing Link
We know that momentum is conserved during the impact. But what about after the collision?
The Logic Chain:
Measure Skid Distance (d)
Use Work-Energy to find velocity just after collision (vf)
Use Momentum to find velocity just before collision (vi)
DISTANCE → SPEED
Friction & Work
The Coefficient
\(\mu\) (Mu): How "sticky" the road is.
Dry Asphalt 0.7 - 0.8
Wet Road 0.4 - 0.6
Icy Surface 0.1 - 0.2
The Work-Energy Theorem:
\[ W = \Delta KE \] \[ F_{fric} \cdot d = \frac{1}{2}mv^2 \] \[ \mu mg \cdot d = \frac{1}{2}mv^2 \]
Notice: Mass cancels out! Speed depends only on friction and distance.
The "Skid-to-Stop" Formula
Post-Impact Velocity
\[ v = \sqrt{2\mu gd} \]
Where g = 9.8 m/s2
Caution:
This only works if the vehicle skids to a complete stop. If they hit something else, there is leftover energy!
Investigator Tip:
Look for "Shadow Skids" – faint marks that appear before the heavy black lines. These indicate the moment brakes were first applied.
The Full Scene
Step 1
Skid Distance
Step 2
Work-Energy (\(v_f\))
Step 3
Momentum (\(v_i\))
"Physics lets us rewind time. Each piece of evidence is a frame in the movie of the accident."
Skid Analysis Teacher Guide Friction Analysis Guide
Lesson 02: Tire Tracks and Speed
Teacher Resource
ID: FOR-TS-002
Instructional Focus
This lesson bridges the gap between Work-Energy and Momentum. Students often struggle to see when to use which law. This lesson clarifies that Friction (Work) happens over a distance (the skid), while Momentum is conserved in an instant (the impact).
Equation: v = √(2μgd)
Common Pitfalls
Units: Ensure students use meters for distance and m/s for velocity. Speed limit signs are in mph/kph; conversion is a common forensic step.
The "Square Root": Many students forget to take the root at the end of the work-energy derivation.
Mass: Students often look for mass to calculate stopping speed. Remind them that mass cancels out in the friction/KE equality.
Instructional Flow
00-10m
Derivation Workshop
Walk students through the derivation on the board: \( \text{Work Done by Friction} = \Delta \text{Kinetic Energy} \). Show how mass (\(m\)) is on both sides and cancels. This is a "mind-blown" moment for many: heavy trucks and light cars skid the same distance if their tires are identical.
10-25m
Slide Presentation
Use the Tire Tracks Slides . Focus on Slide 3 (Coefficient of Friction). Discuss how weather affects \(\mu\) and why investigators must measure the drag factor of the specific road on the day of the crash.
25-45m
Skill Practice: Evidence Sheet
Distribute the Skid Analysis Evidence Sheet . Monitor students as they perform the calculations. Watch for calculator errors with the square root function.
Classroom Demo: The Drag Block
Use a spring scale to drag a wooden block across different surfaces (carpet, sandpaper, smooth tile). Calculate \(\mu\) for each surface: \( \mu = \text{Force of Friction (Scale Reading)} / \text{Normal Force (Weight)} \). This makes the "Drag Factor" concrete for students.
Skid Analysis Evidence Sheet EVIDENCE LOG: SKID MARKS
Forensic Division • Friction & Work Analysis
Log Date
2026-01-17
Lead Investigator:
Badge Number:
1. Determining the Drag Factor (μ)
Investigators used a drag sled to test the road surface. A 20 kg sled required 140 N of force to pull at a constant speed across the asphalt. Calculate the coefficient of friction (\(\mu\)).
\( F_{fric} = \mu \cdot F_N \)
\( F_N = m \cdot g \) (use g = 9.8)
Calculation Area
μ =
2. Impact Speed Calculation
SCENARIO: OAK STREET COLLISION
Vehicle A struck a parked car and then skidded 22 meters to a final stop. The road was dry (\(\mu = 0.75\)).
A) Use the formula \( v = \sqrt{2\mu gd} \) to find the velocity of Vehicle A immediately after the impact.
vpost =
m/s
B) Speed Limit Conversion: Multiply your answer by 2.24 to convert m/s to Miles Per Hour (mph).
Speed in MPH =
3. Evidence Interpretation
Investigator Note:
"Upon arrival, I noticed the skid marks were curved , indicating the driver was attempting to steer while braking. Does the curvature of a skid mark affect the 'd' value in our formula?"
Rain Warning
If it begins to rain before the scene is processed, what happens to the μ value? How does this make reconstruction more difficult?
Calculations Verified
Evidence Certified
Vector Vision Slides VECTOR VISION
2D Momentum & Glancing Blows
SYSTEM STATUS: ANALYZING COMPONENTS...
The Glancing Blow
Not all crashes are head-on. Many collisions happen at angles, sending vehicles spinning off into the X and Y planes .
The Golden Rule:
Momentum is conserved independently in each direction.
T-BONE INTERSECTION MODEL
Breaking it Down
X-Momentum
The sum of all horizontal momentum before = the sum after.
\[ \sum p_{x,i} = \sum p_{x,f} \]
Y-Momentum
The sum of all vertical momentum before = the sum after.
\[ \sum p_{y,i} = \sum p_{y,f} \]
Investigator Tip: Use Trigonometry to find the components!
\( p_x = p \cos(\theta) \) \( p_y = p \sin(\theta) \)
The Pool Table Analogy
Professional pool players use 2D momentum conservation intuitively.
Offset hits: Control the final angle.Elastic collisions: Minimal energy lost.Predictable paths: If you know the mass and velocity of the cue ball, the rest is geometry.
Simulating the Crash:
Today, you will use a virtual collision lab to test how mass and angle affect the "scatter" of the vehicles.
Vector Synthesis
Total Momentum Vector
By combining our X and Y calculations, we find the Magnitude and Direction of the impact.
X
Momentum
Y
Momentum
Result: The True Path of the Collision
Simulation Inquiry Guide Vector Lab Guide
Lesson 03: Glancing Blows and Vectors
Simulation Facilitator
ID: FOR-TS-003
Instructional Intent
Transitioning from 1D to 2D is a major conceptual leap. This lesson avoids heavy trigonometry (which can lose students) and focuses on the qualitative understanding of vector components. Students use a simulator to "see" how x-momentum and y-momentum are preserved separately.
Recommended Tools
PhET Collision Lab (2D)
The Physics Aviary: 2D Collision
Graph Paper / Protractor
Teacher "Watch-Fors"
The "Static" Object: If one car is hit while parked, students often forget it still gains momentum in the direction of the impact.
Vector Addition: Remind them that vectors add "tip-to-tail," not just by adding their lengths together like scalars.
Simulation Walkthrough
Phase 1: The Head-On (Recap)
Have students set up a simple 1D crash. Verify that the combined mass behaves predictably. This builds confidence before adding angles.
Phase 2: The Offset Impact
Adjust the impact parameter so the cars "glance" off each other. Ask: "Did the total speed of the system change? How about the total momentum?"
Key Question: If Car A had 10 units of X-momentum before, and after the crash it has 4 units of X-momentum, where did the other 6 units go? (Answer: Car B).
Phase 3: Measuring Angles
Have students record the angle of scatter for both vehicles. This data is what investigators find at the scene using debris fields and skid tracks.
The "Expert" Challenge
Give students a "mystery" crash result (angles and final speeds) and ask them to determine if the car that hit was going Fast , Medium , or Slow . Let them use trial-and-error in the simulation to match the scene. This develops an "investigator's intuition" for momentum.
Glancing Blow Patterns Worksheet VECTOR LOG: GLANCING BLOWS
Forensic Data Sheet • Unit 03
Investigator Name:
Station ID:
1. Component Deconstruction
Draw the horizontal (x) and vertical (y) components for the following momentum vectors. Use a ruler for straight lines.
Vector A (30° Angle)
Sketch px and py above.
Vector B (110° Angle)
Sketch px and py above.
2. Simulation Results
Run a "T-Bone" collision in the simulator (Car 1 moving East, Car 2 stationary). Adjust the mass of Car 1 and record the scatter angles.
Trial # Car 1 Mass (kg) Car 1 Angle (θ1) Car 2 Angle (θ2) 1 1500 2 3000
Observation Question:
How did increasing the mass of the striking car (Trial 2) change the scatter angle of the car that was hit?
3. Expert Interpretation
"Two vehicles collide at a 4-way stop. Vehicle 1 was heading North. Vehicle 2 was heading East. After the crash, both vehicles slide together towards the North-East ."
A) Vector Sketch:
Sketch the combined final momentum vector.
B) Analysis:
If the final path is more North than East (e.g., a 70° angle), which vehicle likely had more momentum before the impact?
The Big Crash Slides Top Secret REPORT NO. 99-RECON
ACCIDENT RECONSTRUCTION
Case Analysis: The High-Stakes Synthesis
Task Force: Forensic Physics Unit
The Mission
You have been handed a complete Evidence Dossier for a multi-vehicle collision.
Your Goal:
Calculate pre-collision speeds.
Identify which driver violated traffic laws.
Defend your findings with physics.
Evidence Provided:
Scene Map & Final Positions
Post-Impact Skid Lengths
Vehicle Curb Weights (Mass)
Road Conditions (μ)
The Recon Protocol
1. Extract Data
Find the m1, m2, and μ from the case file.
2. Post-Impact
Use \( v = \sqrt{2\mu gd} \) for both vehicles.
3. Pre-Impact
Apply momentum conservation to find initial speeds.
Scientific Testimony
"Math doesn't lie, but people do."
In the final phase (tomorrow), you will act as Expert Witnesses . You must explain your calculations so clearly that even a jury with no physics background can understand them.
Key Terms for Your Report:
Momentum
Vector
Inelastic
Friction
Coefficient
Conservation
Open Your Dossier
The investigation begins now.
Gather Evidence
Run Calculations
Find the Truth
Final Crash Dossier Project Guide Classified Evidence
Official Case Dossier
FILE REF: COLLISION-94-ALPHA
Dispatch Summary
"Responding units arrived at the intersection of Maple and 4th. A 2023 Heavy SUV (Vehicle A) and a 2019 Compact Sedan (Vehicle B) were involved in a T-Bone collision. Vehicle A was traveling East; Vehicle B was traveling North. Upon impact, the vehicles locked together and slid as one unit to their final resting position. No brake marks were observed before the impact, indicating no significant deceleration prior to the crash."
Vehicle Specifications
Mass of Vehicle A (mA) 2,400 kg
Mass of Vehicle B (mB) 1,200 kg
Environmental Data
Road Condition Wet Asphalt
Drag Factor (μ) 0.50
Scene Evidence (Post-Impact)
The combined mass of the vehicles slid for 18.4 meters after the collision before stopping. The path of the slide was measured at an angle of 33.7° North of East .
Note: At this angle, the final momentum consists of both X (East) and Y (North) components.
Final Resting Position
The Violation
The speed limit on both streets is 35 mph (15.6 m/s) . Which driver(s) exceeded the speed limit? Use your reconstruction to prove your answer.
Investigator Calculation Workspace
Step 1: Calculate Final Velocity (vf) of the combined system
Step 2: X-Momentum (East) Calculation
Step 3: Y-Momentum (North) Calculation
Final Conclusion: Who is at fault? Reconstruction Rubric Assessment Guide Project Rubric
Lesson 04: The Big Crash Reconstruction
Assessment Tool
ID: FOR-TS-004
Criteria Exceptional (10 pts) Proficient (7 pts) Developing (4 pts) Data Extraction All variables (m, μ, d, θ) identified correctly with appropriate units. Variables identified correctly, but minor unit errors present. Missing multiple key variables from the dossier. Work-Energy Analysis Post-impact velocity (vf) calculated perfectly using correct formula. Correct formula used, but minor calculation error (e.g., square root). Incorrect formula applied or vf significantly off. Vector Components Momentum broken into X/Y components using trig with total accuracy. Correct approach to components, but math error in trig values. Failure to differentiate between X and Y planes. Final Reconstruction Determined fault based on correct speed limit conversion (m/s to mph). Correct fault identification, but explanation is logically weak. Incorrectly identified driver at fault or no conclusion provided.
Case Alpha-94 Solution Key
1. Post-Impact Speed (vf):
\( v_f = \sqrt{2 \cdot 0.5 \cdot 9.8 \cdot 18.4} \approx 13.43 \text{ m/s} \)
2. Total Post-Impact Momentum (ptotal):
\( (2400+1200) \cdot 13.43 \approx 48,348 \text{ kg·m/s} \)
3. Initial Speeds:
Vehicle A (East): \( v_{Ai} \approx 16.75 \text{ m/s} \) (~37.5 mph) → Speeding
Vehicle B (North): \( v_{Bi} \approx 22.3 \text{ m/s} \) (~50 mph) → Speeding
*Note: Both vehicles were above the 35 mph limit.
*Partial credit should be awarded for "following through" with a calculation error if the physics logic remains consistent. The goal is to evaluate their understanding of momentum conservation.
Courtroom Protocol Slides Expert Witness
Forensic Physics Testimony
What is an Expert Witness?
Unlike a regular witness who testifies about what they saw , an expert witness testifies about what they know .
Your Duty:
"To provide impartial, scientific analysis to help the jury understand the evidence."
Credentials:
"I have a background in Physics and have reconstructed 100+ accident scenes."
Under Fire
The Attack:
"How do you know the road wasn't slicker than 0.50?"
Your Defense:
Cite the official weather report and standard drag-sled testing protocols.
The Attack:
"Isn't it true momentum is only for elastic collisions?"
Your Defense:
Clarify that momentum is conserved in all collisions, regardless of elasticity.
The Attack:
"Is your math really precise enough for this?"
Your Defense:
Show your work. Explain that physics laws are the most precise tools we have.
Speaking to the Jury
Avoid Jargon:
"The inelastic system's scalar magnitude of post-impact KE was..."
Try This Instead:
"When the cars locked together, they formed a single heavy object that required a lot of friction to stop."
Use Visuals:
"If we look at this vector diagram, you can see that more energy came from the North than from the West. That proves Vehicle B was the faster car."
Order in the Court
Are you prepared to stand by your calculations?
I. Opening Statements
II. Expert Testimony
III. Verdict
Mock Trial Facilitation Guide Mock Trial Facilitator
Lesson 05: Expert Witness Testimony
Teacher Resource
ID: FOR-TS-005
Communication of Science
The culminating experience of this sequence isn't just about the math; it's about the application and communication of that math. Students must defend their findings against scrutiny, simulating the real-world pressure forensic engineers face.
Team Roles
Lead Expert: Explains the main vi calculation.Friction Analyst: Explains the μ and skid distance.Vector Specialist: Explains the scatter angles.
Legal Adversaries
Assign one group to be the "Defense" for Vehicle A and another for Vehicle B. They must try to poke holes in each other's math.
The "Jury"
Students not currently testifying act as the jury. They must vote on who is at fault based only on the evidence presented.
Courtroom Protocol
1. Direct Examination
The "Prosecution" or Team Lead asks their own experts questions. "Officer, tell the jury how you determined the speed of the red car." Experts present their posters/worksheets.
2. Cross-Examination
The opposing team asks challenging questions. "Isn't it true you ignored the fact that it was raining?" Experts must defend their logic using physics laws.
3. Closing Statement
One student summarizes: "The physics shows that Vehicle B had twice the momentum of Vehicle A. Therefore, B must have been speeding."
Observation Checklist
Used terms like 'Conservation of Momentum' correctly.
Referred to specific evidence from the dossier.
Remained professional/scientific under pressure.
Effectively explained X/Y components to 'laypeople'.
Witness Testimony Notes Expert Witness Prep
Trial Session 05 • Testimony Outline
Name of Expert
Area of Expertise (Friction, Momentum, or Vectors)
I. Direct Examination Prep
Plan how you will answer the following questions during your opening testimony.
1. "Expert, can you explain the Law of Conservation of Momentum in your own words for the jury?"
2. "Looking at Case Alpha-94, what specific evidence did you use to calculate the initial speeds?"
3. "Walk us through your calculation for Vehicle A. What was the result?"
II. Cross-Examination Defense
Anticipate what the "Defense Attorney" (the other team) will ask to try to discredit your work.
Potential Challenge #1:
"Your calculation assumes a perfect T-Bone collision. Isn't it possible the angle was slightly different?"
Your Rebuttal:
Potential Challenge #2:
"Friction varies. How can you be 100% sure about your 'Drag Factor' of 0.50?"
Your Rebuttal:
The Verdict
Based on your testimony, which of the following is your professional conclusion? (Check one)
Vehicle A was the sole violator.
Vehicle B was the sole violator.
Both vehicles were in violation.
Evidence is inconclusive.
