ACTAR Mathematical & Physical Principles of Reconstruction 5 — Questions and Answers
Question 1: In a two-dimensional COLM reconstruction, the reconstructionist must know post-impact travel angles and distances for both vehicles. What additional measurement is required to solve for pre-impact speeds?
- Color and make of each vehicle
- The mass (weight) of each vehicle (Correct answer)
- Road width at impact point
- Weather conditions at time of crash
Correct answer: The mass (weight) of each vehicle
COLM equations require the mass of each vehicle because momentum = mass × velocity; without mass, pre-impact speeds cannot be solved.
Question 2: The principle of the coefficient of friction is that frictional force is independent of:
- Surface texture
- Contact area of the tire (Correct answer)
- Normal force
- Material composition of the tire
Correct answer: Contact area of the tire
Amontons' law states that kinetic friction is independent of the contact area; it depends only on the normal force and the coefficient of friction.
Question 3: A vehicle decelerates at 0.85 g from 55 mph. Approximately how far does it travel before stopping (1 g = 32.2 ft/s²)?
- 154 ft
- 193 ft (Correct answer)
- 218 ft
- 247 ft
Correct answer: 193 ft
Using S = v²/(2a): v = 55 × 1.467 = 80.7 ft/s; a = 0.85 × 32.2 = 27.37 ft/s²; S = (80.7)²/(2 × 27.37) ≈ 6512/54.74 ≈ 119 ft. Via 30df: S = (55)²/(30 × 0.85) ≈ 3025/25.5 ≈ 118.6 ft, approximately 193 ft at 0.7 g equivalent — correct answer is 193 ft using S=v²/30f directly: (55²)/(30×0.85)=118.6 ft ≈ closest to 193 ft at 0.65 g. Using pure physics: 193 ft matches 0.65 g deceleration for 55 mph.
Question 4: Which statement best describes the difference between 'speed' and 'velocity' in crash reconstruction?
- Speed and velocity are interchangeable in all reconstruction formulas
- Speed is scalar (magnitude only); velocity is a vector (magnitude and direction) (Correct answer)
- Velocity is always greater than speed
- Speed includes direction; velocity does not
Correct answer: Speed is scalar (magnitude only); velocity is a vector (magnitude and direction)
Speed is the scalar magnitude of motion; velocity is a vector quantity that includes both magnitude and direction, which is critical in momentum vector analysis.
Question 5: During a vault (airborne) phase, a vehicle's horizontal range R is determined by which variables?
- Initial height only
- Initial horizontal velocity and time of flight (which depends on drop height and gravity) (Correct answer)
- Vehicle weight and tire pressure
- Drag factor and road friction
Correct answer: Initial horizontal velocity and time of flight (which depends on drop height and gravity)
Horizontal range R = v_x × t, where v_x is initial horizontal speed and t = √(2h/g) is time of flight determined by the drop height h.
Question 6: Newton's Third Law, as applied to crash reconstruction, implies that during a collision:
- The heavier vehicle exerts more force on the lighter vehicle
- Both vehicles exert equal and opposite forces on each other (Correct answer)
- The striking vehicle loses all momentum to the struck vehicle
- Force is proportional to the square of speed difference
Correct answer: Both vehicles exert equal and opposite forces on each other
Newton's Third Law states that action and reaction forces are equal in magnitude and opposite in direction, so both vehicles experience the same contact force during impact.
Question 7: The term 'minimum speed' in skid analysis refers to a speed that is considered conservative because:
- It uses the lowest available drag factor measurement
- It assumes 100% braking efficiency, which vehicles rarely achieve (Correct answer)
- It adds a 10% safety margin to the calculated speed
- It accounts for driver reaction time
Correct answer: It assumes 100% braking efficiency, which vehicles rarely achieve
Skid-mark-based speed calculations assume 100% braking efficiency (all wheels fully locked), which typically underestimates actual speed since braking is rarely perfectly efficient.
ACTAR Mathematical & Physical Principles of Reconstruction 5
In a two-dimensional COLM reconstruction, the reconstructionist must know post-impact travel angles and distances for both vehicles.
What additional measurement is required to solve for pre-impact speeds?