ACTAR Crash Dynamics 5 — Questions and Answers
Question 1: During a collinear rear-end collision (both vehicles traveling in the same direction), which formula correctly represents the conservation of momentum?
- m₁v₁ + m₂v₂ = m₁v₁' - m₂v₂'
- m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' (Correct answer)
- m₁v₁ - m₂v₂ = (m₁ + m₂)v'
- m₁v₁² + m₂v₂² = m₁v₁'² + m₂v₂'²
Correct answer: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
Conservation of momentum requires that the total momentum before impact equals total momentum after: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' (with consistent sign convention).
Question 2: Which crash phase is characterized by the vehicles moving together at a common velocity, immediately before they begin to separate?
- Pre-crash phase
- Maximum engagement (common velocity) point (Correct answer)
- Restitution phase
- Post-separation phase
Correct answer: Maximum engagement (common velocity) point
At the point of maximum engagement, both vehicles momentarily share a common velocity before elastic recovery forces cause separation in the restitution phase.
Question 3: A vehicle with a center of gravity height of 0.6 m and a track width of 1.8 m is cornering. The approximate lateral acceleration threshold at which tip-over begins is approximately:
- 0.25 g
- 0.75 g
- 1.50 g (Correct answer)
- 2.25 g
Correct answer: 1.50 g
The static rollover threshold ≈ track width / (2 × CG height) = 1.8 / (2 × 0.6) = 1.5 g; below this, the vehicle slides before tipping.
Question 4: When two vehicles of different masses collide and stick together (perfectly plastic collision), post-impact velocity is calculated using:
- Average of both pre-impact speeds
- (m₁v₁ + m₂v₂) / (m₁ + m₂) (Correct answer)
- v₁ × v₂ / (v₁ + v₂)
- ½(m₁ + m₂)(v₁² + v₂²)
Correct answer: (m₁v₁ + m₂v₂) / (m₁ + m₂)
In a perfectly plastic (inelastic) collision where objects stick together, the common post-impact velocity = total pre-impact momentum divided by total mass.
Question 5: An analyst finds that a vehicle's tires left yaw marks before impact. The primary information yaw marks provide for reconstruction is:
- The braking force coefficient at the moment of impact
- The minimum speed of the vehicle at the start of the yaw, via critical curve speed analysis (Correct answer)
- The weight distribution across all four tires
- The steering angle at time of impact
Correct answer: The minimum speed of the vehicle at the start of the yaw, via critical curve speed analysis
Yaw mark radius, combined with the road's friction coefficient, allows calculation of the minimum critical curve speed using the formula v = √(f × g × r).
Question 6: In a friction-based energy analysis, the 'drag factor' used for a sliding vehicle should ideally be determined by:
- Looking up a standard table for the road surface type
- Conducting test skids at or near the scene under similar conditions (Correct answer)
- Using the vehicle manufacturer's braking coefficient
- Defaulting to 0.7 for all dry paved surfaces
Correct answer: Conducting test skids at or near the scene under similar conditions
Test skids performed at or near the collision scene under similar temperature, surface, and tire conditions provide the most accurate drag factor for that specific event.
Question 7: Which of the following best explains why airbag deployment data (SDM/EDR) must be interpreted carefully in speed reconstruction?
- EDR data is always recorded in metric units regardless of vehicle origin
- EDR records delta-V from the onset of the crash event, which may not equal pre-impact speed if the vehicle was already decelerating (Correct answer)
- Airbags only deploy in head-on collisions, limiting EDR data utility
- EDR data cannot be legally admitted as evidence in US courts
Correct answer: EDR records delta-V from the onset of the crash event, which may not equal pre-impact speed if the vehicle was already decelerating
EDR delta-V recording begins at crash onset; if the vehicle was already braking before the sensor threshold, pre-braking speed will be higher than the EDR-recorded delta-V suggests.
ACTAR Crash Dynamics 5
During a collinear rear-end collision (both vehicles traveling in the same direction), which formula correctly represents the conservation of momentum?