ACTAR Mathematical & Physical Principles of Reconstruction 2 — Questions and Answers
Question 1: A vehicle skids to a stop leaving 120 feet of skid marks on a road with a drag factor of 0.75. Using the skid-to-stop formula, what was the approximate minimum speed?
- 42.5 mph
- 51.5 mph (Correct answer)
- 56.6 mph
- 63.2 mph
Correct answer: 51.5 mph
Using S = √(30 × d × f) = √(30 × 120 × 0.75) = √2700 ≈ 51.96 mph, which rounds to approximately 51.5 mph.
Question 2: In projectile motion analysis of a vehicle that launches off a cliff, which two components of initial velocity are treated as independent?
- Vertical and angular
- Horizontal and vertical (Correct answer)
- Radial and tangential
- Longitudinal and lateral
Correct answer: Horizontal and vertical
Projectile motion treats horizontal velocity as constant (no air resistance assumed) and vertical velocity as independently accelerated by gravity.
Question 3: What is the centripetal acceleration of a vehicle traveling at 60 ft/s around a curve with a radius of 300 feet?
- 6.0 ft/s²
- 9.8 ft/s²
- 12.0 ft/s² (Correct answer)
- 18.0 ft/s²
Correct answer: 12.0 ft/s²
Centripetal acceleration a = v²/r = (60)²/300 = 3600/300 = 12.0 ft/s².
Question 4: Conservation of momentum in a two-vehicle collision is valid only when:
- Both vehicles are the same mass
- No external forces act on the system during impact (Correct answer)
- Collision is perfectly elastic
- Vehicles travel in the same direction before impact
Correct answer: No external forces act on the system during impact
Conservation of momentum applies when the net external force on the system is zero, meaning no significant external forces act during the brief impact interval.
Question 5: A vehicle with a weight of 3,200 lbs has a coefficient of friction of 0.72 with the road. What is the maximum frictional braking force available?
- 1,728 lbs
- 2,304 lbs (Correct answer)
- 3,200 lbs
- 4,444 lbs
Correct answer: 2,304 lbs
Frictional force = weight × coefficient of friction = 3,200 × 0.72 = 2,304 lbs.
Question 6: When calculating the speed from yaw (critical curve) marks, the reconstrutionist uses which primary formula?
- S = √(15 × r × e+f) (Correct answer)
- S = √(30 × d × f)
- S = √(2 × a × d)
- S = (m1v1 + m2v2)/(m1 + m2)
Correct answer: S = √(15 × r × e+f)
Critical speed for a yaw mark is S = √(15 × r × (e + f)), where r is the radius of curvature, e is superelevation, and f is side friction.
Question 7: The coefficient of restitution (e) for a perfectly plastic (inelastic) collision equals:
- 1.0
- 0.5
- 0.0 (Correct answer)
- -1.0
Correct answer: 0.0
A perfectly plastic collision means the objects stick together with no rebound, so e = 0, indicating zero relative velocity after impact.
ACTAR Mathematical & Physical Principles of Reconstruction 2
A vehicle skids to a stop leaving 120 feet of skid marks on a road with a drag factor of 0.75.
Using the skid-to-stop formula, what was the approximate minimum speed?