Momentum Mechanics Slides Momentum Mechanics
The Physics of Impact & Safety
Crash Test Lab Module 03
Recall the Lab
In our Impact Investigation, we found that:
Higher ramp height (more speed) = Further slide.
More cart mass = Further slide.
"We measured the distance the box moved, but what was happening during the collision?"
CART
TISSUE BOX
Distance = Work / Friction
The Secret of the Sensor
Sensor Data Analysis
What happens when two carts collide?
We see two force curves that are mirror images of each other.
Newton's 3rd Law:
"For every action, there is an equal and opposite reaction."
The magnitude of the force on each object is identical, even if one object is much larger!
Time (ms)
Force (N)
Cart A Force Cart B Force
Mass & Fatality
If forces are equal, why are outcomes different? Real-world crash data shows risk depends on vehicle mass.
Fatality Risk in Collisions
Vehicle Pairs Risk Factor Large SUV vs SUV 1.0x Large SUV vs Sedan 4.2x Higher Sedan vs Large SUV 0.3x Lower
Physics Check:
Forces are the same, but acceleration is higher for the smaller vehicle:
a = F / m
"Smaller mass = Larger change in speed."
Defining Momentum
p
=
m
×
v
Momentum
(kg · m/s)
Mass
(kg)
Velocity
(m/s)
Momentum is "inertia in motion." The more momentum an object has, the harder it is to stop.
Conservation Law
The total momentum before a collision equals the total momentum after.
Total Pinitial = Total Pfinal
If Cart A loses momentum...
...Cart B must gain the exact same amount.
Momentum Transfer
10 units
0 units
2 units
8 units
Total: 10 → Total: 10
Collision Logic Worksheet Collision Logic
Momentum Mechanics Module
Name:
Date:
1
Experimental Evidence
In your previous lab, you measured how far a tissue box moved after being hit by a cart. We now know that Momentum (p = mv) is what the cart carried into that collision.
Speed vs. Distance
When you doubled the speed (v), the box moved much further. Why?
Mass vs. Distance
When you added mass (m) to the cart, the box moved further. Why?
Thinking Question:
If a 0.5 kg cart is moving at 2 m/s, what is its momentum?
Show your work using p = m × v
2
Fatality Data Analysis
Relative Risk of Death by Vehicle Pair
Collision Pair (Vehicle A vs Vehicle B) Risk Factor for Driver B Large SUV vs Small Sedan 4.2x (Highly Dangerous) Small Sedan vs Small Sedan 1.0x (Baseline) Large SUV vs Large SUV 1.0x (Baseline)
Analysis Prompt:
Newton's 3rd Law states the forces between a Large Truck and a Small Car are equal during a crash. Use the concept of mass and acceleration (a = F / m) to explain why the person in the smaller car is at greater risk.
3
Conservation Models
In a collision between two objects, the total momentum before equals the total momentum after .
m1v1 + m2v2 = m1v1' + m2v2'
Scenario A: The Rear-End Collision
A 2,000 kg truck moving at 10 m/s hits a stationary 1,000 kg car (0 m/s). After the hit, the truck slows down to 4 m/s.
1. Calculate Total Momentum BEFORE:
2. Calculate the Car's Final Velocity:
Scenario B: The Head-On Mystery
Two identical 1.5 kg carts collide head-on. Cart 1 is moving at +2 m/s. Cart 2 is moving at -2 m/s. They hit and stick together (velocity = 0).
What was the total momentum of the system before the crash? Explain your reasoning.
Scenario C: Forensic Engineering
Investigators find a car hit a brick wall. The mass of the car is 1,200 kg and the force of impact was 48,000 N acting over 0.2 seconds.
Solve for the change in velocity (Δv) using the Impulse-Momentum equation: F · t = m · Δv
Physics Fact
Momentum is conserved. Forces are equal. Risk depends on mass.
Collision Logic Answer Key Answer Key
Collision Logic • Teacher Resource
CONFIDENTIAL
1. Experimental Evidence
Speed vs. Distance
Increasing speed increases momentum (\(p=mv\)). This gives the cart more "stopping distance" requirement as it does more work on the box against friction.
Mass vs. Distance
Increasing mass increases momentum proportionally. A heavier cart has more inertia in motion and requires more force/distance to be brought to rest.
Thinking Question:
\(p = 0.5 \text{ kg} \times 2 \text{ m/s} = \mathbf{1.0 \text{ kg·m/s}}\)
2. Fatality Data Analysis
Newton's 3rd Law & Acceleration Explanation:
While the Force (F) is the same for both vehicles, Acceleration (a) is determined by \(a = F/m\).
For the Large Truck, \(m\) is big, so \(a\) is small. Occupants feel a gradual change.
For the Small Car, \(m\) is small, so \(a\) is very large. This high acceleration causes severe injury/trauma to the body as it changes speed almost instantly.
3. Conservation Models
Scenario A: Rear-End
1. Total Before: \(p_{truck} = 2000 \times 10 = 20,000 \text{ kg·m/s}\). \(p_{car} = 1000 \times 0 = 0\). Total = 20,000.
2. Car's Velocity: 20,000 (Before) = \((2000 \times 4) + (1000 \times v_{final})\)
20,000 = 8,000 + 1000v \(\rightarrow\) 12,000 = 1000v \(\rightarrow\) v = 12 m/s.
Scenario B: Head-On
Total Momentum is 0 kg·m/s . Momentum is a vector. Cart 1 has \(+3 \text{ kg·m/s}\) and Cart 2 has \(-3 \text{ kg·m/s}\). They cancel out completely.
Scenario C: Forensics
\(F \cdot t = m \cdot \Delta v\)
\(48,000 \text{ N} \times 0.2 \text{ s} = 1,200 \text{ kg} \times \Delta v\)
\(9,600 = 1,200 \Delta v\)
\(\Delta v = 9,600 / 1,200 = \mathbf{8 \text{ m/s}}\) (Approx 18 mph).
Instructional Tip
Emphasize that "Conservation" means the system doesn't lose anything, even if individual parts change drastically. Use the "Head-On" example to discuss how energy might turn into heat/deformation even while momentum is zero.
Fatal Physics Teacher Guide Fatal Physics Guide
Teacher Facilitation • Unit Synthesis
Learning Goals
Physics Concepts
Newton's 3rd Law: Equal and opposite forces in all collisions regardless of mass.
Momentum: p = mv as a measure of an object's "unstoppability".
Conservation: System momentum remains constant before and after impact.
Real-World Application
Vehicle Safety: Understanding why lighter vehicles have higher driver fatality risks.
Forensics: Using crash data and delta-v (speed change) to reconstruct collisions.
Discussion Prompts
The Sensor Surprise:
"If a fly hits a semi-truck windshield, which one experienced more force?"
Teacher Note: Students will intuitively say the fly. Pivot to the sensor data. The forces are identical; the fly just has far less mass to handle the acceleration of the impact.
Safety vs. Mass:
"Why do we feel 'safer' in a large SUV even though it takes much longer to brake than a small car?"
Teacher Note: Connect back to the Momentum formula. More mass = more momentum at the same speed. In a car-vs-car collision, the heavier car forces the lighter one to change speed more violently.
Content Deep-Dive
Fatality Data Context
The 4.2x risk multiplier for small cars vs. large SUVs is based on real-world crash statistics from organizations like IIHS. This is driven by Newton's Second Law (a = F/m). In a collision, the velocity change (delta-v) of the smaller car is drastically higher than the SUV's. This rapid deceleration causes internal injury, even if the car's frame stays intact.
Conservation Misconceptions
Students often think momentum is "destroyed" if objects stop. Remind them that momentum is a vector . If two objects of equal and opposite momentum collide head-on and stop, the total system momentum was zero before and remains zero after.
Differentiation & Extension
Support Strategies
Focus on the conceptual "heavy vs. fast" trade-off. Use physical models like billiard balls to show momentum transfer before diving into the math equations.
Extension Ideas
Challenge advanced students to research "crumple zones" and explain how they extend collision time (t) to reduce impact force (F) while keeping momentum change the same.
Impact Investigation Lab Handout Impact Investigation
CIB: Crash Investigation Bureau // Lab Handout
Name: ______________________
Date: ________________
Mission Objective
Determine how Mass and Speed change collision force by measuring the Sliding Distance of a standard tissue box.
Set Up Protocol
1. Place Tissue Box exactly at end of ramp (0 cm distance ).
2. Measure total cm the box slides from the end of the ramp.
1
Part A: Impact Speed (Varying Ramp Height)
Release Height Trial 1 (cm) Trial 2 (cm) Avg. Low (10cm) Med (25cm) High (40cm)
2
Part B: Vehicle Mass (Constant 25cm Height)
Mass Added Trial 1 (cm) Trial 2 (cm) Avg. 0 (Empty) 4 Washers 8 Washers
Post-Collision Analysis
1. Mathematical Patterns
As Speed or Mass increases, what happens to the distance? Is it a direct relationship?
2. Dramatic Effect
Which variable caused a bigger jump in distance?
3. Tissue Box Factor
Does "squishiness" change the slide distance? Why?
Protocol SECURE-9821 // Lab Station Rotation
Calibrated-Data // One-Page Report
Virtual Impact Lab Handout Virtual Impact Lab
CIB: Crash Investigation Bureau // Remote Evidence Module
Name: ______________________
Date: ________________
Remote Setup Protocol
Measure displacement from the Red Line (0cm) , which is the exact edge of the ramp.
Set A: Release height was varied (10, 25, 40cm) to change the impact speed.Set B: Height was fixed at 25cm while washers were added to increase cart mass.
Setup A: Variable Speed
Setup B: Variable Mass
A
Set 01 Evidence: Impact Speed
Low
0
30
60
80
90
120
150
Box
Med
0
30
60
90
105
120
Box
High
0
30
60
90
120
122
Box
B
Set 02 Evidence: Vehicle Mass
Empty
0
50
100
150
Box
4 Washers
0
50
115
150
Box
8 Washers
0
50
120
150
Box
Evidence Data Log
Trial Variable Measured Distance (cm) Set A: Low (10cm) Set A: Med (25cm) Set A: High (40cm) Set B: Empty Set B: 4 Washers Set B: 8 Washers
Investigation Summary
Does your data show a proportional relationship? How does speed affect force proxy differently than mass?
CIB Digital Archive // One-Page Report
V.2026.9
Impact Investigation Slides Field Operations Briefing
Impact
Investigation
Analyzing collision physics with the "Tissue Box" test.
CIB Division
Unit 3: Momentum & Collisions
The Laboratory Setup
1
Place the Tissue Box at the very bottom of the ramp (0cm gap ).
2
Set the Release Height (Low, Med, or High).
3
Release Cart and measure the box's Slide Distance .
Box
Cart
0 CM LINE
Calibration View
Station Rotation
Team A: The Lab
Head to your assigned Crash Stations . Perform the tissue box impact trials and record your data in the handout.
Focus: Data Accuracy & Safe Testing
Team B: The Desk
Stay at your desks and complete the Stopping Power Worksheet . Solve for reaction time and braking distance.
Focus: Mathematical Modeling
Swap after 25 Minutes
Physics: Proxies & Data
Independent
Speed: Control with HeightMass: Control with Washers
Dependent
We measure Sliding Distance (cm) .
This is our proxy for the Impact Force and energy transfer.
Virtual Impact Lab Answer Key Virtual Impact Lab
CIB: Crash Investigation Bureau // Teacher Evidence Key
Master Key
Experimental Context
Collision data collected using the ramp release method. Impact energy is measured by the displacement of a tissue box sitting at the 0cm red line .
Red line marks the
Set A: Speed (Varying Ramp Height)
Set B: Mass (Washers inside Cart)
A
Evidence Set 01: Variable Speed
Low (10cm)
80 cm
Med (25cm)
105 cm
High (40cm)
122 cm
Note: This empirical data reflects diminishing returns at higher speeds, likely due to increased box compression (the "crumple zone" effect) and air resistance at higher velocities.
B
Evidence Set 02: Variable Mass
Empty
100 cm
4 Washers
115 cm
8 Washers
120 cm
Investigation Summary: Sample Answer
The data confirms that both Mass and Speed increase collision energy, though the relationships are complex in real-world testing. Increasing height from 10cm to 40cm resulted in a significant increase in sliding distance (80cm to 122cm). This demonstrates that vehicles with more potential energy (higher release) transfer more work to the target box during impact.
CIB REMOTE STANDARD VERIFICATION // Teacher Answer Key
Stopping Power Worksheet Stopping Power
CIB: Crash Investigation Bureau // Concept Module 01-A
Name: ______________________
Date: ________________
Investigation Brief
Total Stopping Distance = Thinking Distance + Braking Distance.
Speed Check
10 m/s ≈ 22 mph
20 m/s ≈ 45 mph
30 m/s ≈ 67 mph
1
Phase 1: Thinking Distance
Thinking distance depends on Reaction Time . Research shows an alert adult takes 0.75 seconds to react. If distracted, that time doubles .
Alert Driver
At 20 m/s , you react in 0.75 seconds . You travel 15 meters before braking.
Visualization: 15 meters is roughly the length of 1.5 school buses .
Distracted Driver
Distraction doubles reaction time to 1.50 seconds . Predict stats for 20 m/s:
Thinking Time: __________ seconds
Thinking Distance: __________ meters
2
Phase 2: Braking Distance
Once brakes are hit, the car's Kinetic Energy is converted to friction. Doubling your speed quadruples (4x) the braking distance.
Math Challenge
Energy = Speed squared (v2)
A car at 10 m/s brakes in 5 meters . If it speeds up to 20 m/s (double speed), what is the new braking distance?
10 Meters
15 Meters
20 Meters
Specific Ratios for 30 m/s (Highway)
Thinking
Speed × 0.75 seconds
Braking
Speed × 1.50
=
Total Stop
Speed × 2.25
CIB Division // Module 01-A
Page 1 of 2
Crash Risk Analysis
CIB: Crash Investigation Bureau // Module 01-B
Research Lab Application
3
The Processing Chain
Distraction creates Cognitive Load . Your brain must switch context, causing a processing delay.
Step A
PERCEPTION
Step B
Decision
Step C
REACTION
Stopping Power Worksheet Answer Key Stopping Power
CIB: Crash Investigation Bureau // Answer Key 01-A
Teacher Guide // Page 1
1
Phase 1: Thinking Distance
Scenario Analysis: The Double Effect
Distracted Thinking Time:
1.50 Seconds
(0.75s × 2)
Distracted Distance:
30 Meters
(15m × 2)
The Logic: Distance = Speed × Time. Doubling the time (0.75s to 1.50s) at a constant speed (20 m/s) results in exactly double the distance (15m to 30m).
2
Phase 2: Braking Distance
Correct Choice: 20 Meters
20m
The Logic: Speed doubled (10 to 20). The v2 rule states that distance must increase by a factor of 4. Therefore, 5m × 4 = 20 meters.
Highway Multiplier Key (at 30 m/s)
Thinking (0.75 × v) + Braking (1.50 × v) = Alert Total (2.25 × v)
Master Key // Module 01-A
Page 1 of 2
Crash Risk Analysis
CIB: Crash Investigation Bureau // Answer Key 01-B
Teacher Guide // Page 2
3
The Processing Chain
Concept: Task Switching
Sample Answer: Step B is delayed because the brain cannot multitask high-load tasks. It must physically "switch focus" from the phone back to the driving environment. This creates a time gap where the car continues moving without the driver making the decision to stop.
4
Highway Hazards
Highway Thinking Distance: 30 m/s × 1.50s = 45 Meters .
Sample Answer: 45 meters is nearly 4 school buses. At highway speeds (approx 67 mph), the driver travels nearly half a football field before they even move their foot to the brake pedal.
5
The 3-Second Rule
A. Thinking Dist (Distracted):
45 Meters
B. Braking Dist (Highway):
45 Meters
C. Total Stop Distance:
90 Meters
D. 3-Sec Safety Buffer:
90 Meters
Conclusion: The buffer is barely safe for a distracted driver. Since the buffer (90m) matches the total stopping distance (90m) exactly, there is zero margin for error . Any sudden stop by the car ahead will lead to a collision.
Master Key // Module 01-B
Page 2 of 2
Crash Project Brief Handout Project Brief: 03-B
Crash Reconstruction Challenge
Lead Engineering Consultant Teams
The Objective
Your firm has been hired by the National Highway Safety Council to analyze a recent collision between an SUV and a small sedan. While the police have basic measurements, they need a "Physics Reconstruction" to understand exactly what happened during the impact and why the occupants of the sedan faced higher risks.
Task 1: Jigsaw Analysis
Break into Expert Groups to analyze specific sets of evidence: Lab Data, Sensor Graphs, Fatality Stats, and Momentum Models.
Task 2: Synthesis Report
Reunite with your Home Team to combine findings into a comprehensive Safety Reconstruction Report.
Team Roles
Firm Name:
Lab Liaison:
Force Invest:
Risk Stats:
Momentum:
The Incident Data
Incident ID: 2026-X49
Intersection Crash: SUV (2,500 kg) vs Sedan (1,200 kg)
Impact Speed
15 m/s (Both)
EVIDENCE A
Impact Lab Findings
EVIDENCE B
Force-Sensor Data
EVIDENCE C
Fatality Statistics
EVIDENCE D
Momentum Analysis
Project Deliverables
INDIVIDUAL
Robust Expert Notes detailing your evidence analysis session.
TEAM
Completed Synthesis Report combining all four physics perspectives.
RECOMMENDATION
Safety proposal for the National Highway Safety Council.
"Physics reveals the story that sensors can only hint at."
Crash Jigsaw Expert Cards Jigsaw Expert Task Cards
Physics Reconstruction
Expert A: Lab Liaison
Evidence: Displacement Data
Evidence Review:
In our Impact Lab , we found that increasing a cart's mass leads to a proportional increase in displacement of the target.
Cart Mass Box Slide Dist. 0.5 kg ~40 cm 1.0 kg ~85 cm 2.0 kg (SUV Approx) ~175 cm
Team Tasks:
Explain how much further a target slides when mass is doubled.
Connect this to the SUV vs Sedan collision.
Analysis & Peer Teaching Notes:
Expert B: Force Investigator
Evidence: Force-Time Graph
Evidence Review:
Newton's 3rd Law dictates these forces must be equal in magnitude but opposite in direction.
FORCE
TIME (ms)
SUV SEDAN
Team Tasks:
Verify the peak force is the same for both.
Explain: Same force, but why more damage to the sedan?
Analysis & Peer Teaching Notes:
Expert C: Risk Statistician
Evidence: Risk Analysis
Evidence Review:
DRIVER FATALITY RISK
Mass Ratio Risk (Driver B) 1.0 (Equal) 1.0x (Normal) 1.5 (SUV vs Mid) 2.1x Higher 2.1 (Large SUV vs Sedan) 4.2x Higher
Team Tasks:
Explain why vehicle mass correlates to safety risk.
Use a = F / m to justify why mass protects the driver.
Analysis & Peer Teaching Notes:
Expert D: Momentum Modeler
Evidence: System Vectors
Calculations Brief:
Pinitial = Pfinal
(p = m × v)
Case Data: SUV (2,500kg) at 15m/s hits a Sedan (1,200kg) at 15m/s head-on.
Team Tasks:
Calculate the momentum magnitude for each vehicle.
Which direction will the wreckage travel? Why?
Analysis & Momentum Calculations:
Crash Synthesis Report Template Confidential Case Report
Crash Reconstruction Synthesis
Case ID: 2026-X49 (SUV vs. Sedan)
Firm Name & Lead Partners
Write Firm Name & Members Above
Case Summary Data:
SUV Mass: 2,500 kg
Sedan Mass: 1,200 kg
Impact Velocity: 15 m/s
1
The Momentum Exchange
Collaborate with your Momentum Modeler to solve:
Initial Momentum (SUV):
Show calculations: p = m × v
Initial Momentum (Sedan):
Show calculations: p = m × v
System Conclusion:
Which vehicle "won" the momentum exchange? Explain which direction the wreckage moved and why, based on your calculations above.
2
Force Dynamics & Sensors
Collaborate with your Force Investigator and Risk Statistician:
Newton's 3rd Law proves the force on both vehicles was identical. However, the driver safety risk for the sedan was 4.2x higher. Explain this discrepancy using the Acceleration Law (a = F / m) .
3
Lab Evidence Synthesis
Collaborate with your Lab Liaison:
In the Impact Investigation Lab , you observed that increasing mass caused the target to slide further. How does this experimental data support the reconstruction's claim that the SUV posed a greater threat?
4
Engineering Recommendation
National Safety Improvement Proposal
Based on your team's analysis of Momentum Transfer and Mass Ratios , propose one specific engineering change (to vehicles, roads, or laws) to protect drivers of lighter vehicles.
Target Proposal:
Physics Justification (Linking to Momentum/Force Concepts):
Certified Synthesis
Standard Physics Protocol 1.1
Team Lead Signature:
Crash Project Facilitator Guide Project Facilitator Guide
Crash Reconstruction Synthesis • Teacher Resource
Pacing & Flow
Part 1: The Brief
10 Minutes
Present the Case Study. Assign Home Teams (4 students) and hand out the Project Brief.
Part 2: Expert Jigsaw
20 Minutes
Students split into Expert Groups (all Expert As together, etc.) to master their specific evidence card.
Part 3: Synthesis
25 Minutes
Experts return to Home Teams to teach their findings and complete the Synthesis Report.
Expert Key Concepts
Expert A (Lab)
Focus on energy and work . They must translate the "distance" from the lab into the "damage" seen in the real crash. More momentum → more work required to stop.
Expert B (Force)
Counter the misconception that the SUV hits harder. Forces are equal (3rd Law). The effect of the force differs based on mass.
Expert C (Risk)
Focus on Acceleration Traumatic Injury . Large SUV = Big mass → small acceleration. Sedan = Small mass → extreme acceleration.
Expert D (Math)
Calculations: SUV Momentum = 37,500. Sedan Momentum = -18,000. Total = 19,500 in SUV's direction. Wreckage moves with the SUV.
Grading Rubric
Criteria Exceeding (4) Meeting (3) Approaching (2) Physics Accuracy Correctly applies p=mv, 3rd Law, and a=F/m with math support. Correctly identifies laws; minor math errors. Identifies laws but misses the causal links (e.g. why mass matters). Collaboration Expert notes are robust; synthesis report shows input from all 4 roles. Expert notes complete; report mostly synthesizes data. Missing expert notes or report sections. Engineering Rec Recommendation is rooted in reducing force or increasing mass/time. Recommendation is logical but lacks physics justification. Recommendation is generic (e.g. "be more careful").
Facilitation Tip
During the Expert Jigsaw phase, circulate to Expert B (Force) and Expert C (Risk) particularly. Students often struggle to reconcile "Equal Force" with "Unequal Damage." Help them understand that damage is a result of acceleration and work , not just the magnitude of the force itself.
Crash Forensics Packet Handout Official Bureau Records
Crash
Forensics
Unit 3 Investigation: Collisions, Momentum, and Mathematical Modeling for Vehicle Safety.
Investigator
Case ID U3-COLLISION-2026
MODULE 01
Speed & Reaction
Intelligence Briefing: Reaction Distance (d) = Velocity (v) × Time (t)
If you double your speed, you double the distance you travel before you even touch the brake pedal.
1. Calculation Challenge: 0.8s Reaction Time
Velocity: 15 m/s
Show Work:
d = ________ m
Velocity: 30 m/s
Show Work:
d = ________ m
2. Engineering Solutions
List three vehicle features or public policies that could reduce reaction distance .
1
2
3
MODULE 02
The Science of Stopping
Newton's 2nd Law
F = m × a
Force = Mass × Acceleration
Graph: Stopping Performance
Speed
Time
Slope A: Hard Slope B: Light
A. Which slope represents "Hard Braking" (High Force)? Why?
B. If mass increases, what must happen to Force to stop in the same time?
Risk Report: Wet Road Surfaces
Rain decreases friction, which limits the maximum Braking Force (F) a car can apply before tires lose grip.
Physics Analysis
How does lower friction impact stopping distance?
Policy Recommendation
Propose a speed limit change for rainy conditions.
MODULE 03
Momentum Control
Conservation of Momentum
p = m × v
Total Momentum (Before) = Total Momentum (After)
Case A: Rear-End Collision
A small car (1000kg) at 20 m/s hits a stationary van (2000kg). After impact, they stick together. Calculate final velocity.
Final Velocity = ________ m/s
Case B: Force vs. Mass
Explain why occupants in larger-mass vehicles are statistically safer during a head-on collision.
Insight: Contact forces are ALWAYS equal and opposite, but the result (acceleration) depends entirely on mass!
MODULE 04
Final Design Report
Correlation vs. Causality
Does increasing speed cause more deaths, or do they just happen at the same time? Explain.
Crash Forensics Answer Key Teacher Answer Key
CONFIDENTIAL // INTERNAL USE ONLY
Restricted
Unit 3: Collisions & Momentum
Module 1: Speed & Reaction
1. Scenario Analysis Calculations:
15 m/s × 0.8 s = 12 meters
30 m/s × 0.8 s = 24 meters
Key takeaway: Doubling speed exactly doubles reaction distance.
2. Engineering Solutions:
Speed limits (reduces 'v'), Automated Emergency Braking (AEB) systems that reduce 'v' early, Heads-up displays (reduces 't' reaction), Road signs with higher visibility (reduces 't' reaction).
Module 2: Science of Stopping
A. Graph Analysis:
The "Hard Braking" slope is steeper because it shows a greater change in speed over a shorter amount of time. This represents a higher magnitude of negative acceleration (deceleration).
B. F = ma calculation:
If mass triples, the braking force must also triple to achieve the same acceleration (and thus the same stopping time). F is directly proportional to m when a is constant.
Wet Road Challenge:
Distance will increase because maximum F is lower, meaning 'a' will be lower, requiring more distance to reach zero speed. Speed limits should decrease to keep stopping distances within safe margins.
Module 3: Momentum Master
Case A: Rear-End Calculation:
Initial Momentum: 1000kg × 20m/s = 20,000 kg*m/s
Final Velocity: 20,000 / (1000 + 2000) = 6.67 m/s
Case B: Fatality Risk:
Occupants in larger-mass vehicles undergo a much smaller change in velocity (acceleration) during the collision. According to F=ma, the smaller vehicle experiences a much more violent deceleration to conserve the system's momentum.
Module 4: Design Decisions
Correlation vs. Causality:
Correlation: Two things happen at the same time. Causality: One thing directly makes the other thing happen. Example: Cell phone use directly causes distraction (causality), but color of car might only correlate with speed, not cause it.
Final Commission Questions:
1. High mass trucks have massive momentum even at low speed. Reducing speed limits helps keep the total momentum manageable for city infrastructure and safety. 2. Student answers will vary (e.g., eye-tracking sensors that alarm if a driver looks away from the road for >2 seconds).
