ACTAR Mathematical & Physical Principles of Reconstruction 3 β Questions and Answers
Question 1: A vehicle traveling on a banked curve with a superelevation of 0.06 and a side friction factor of 0.65 negotiates a curve of 500-foot radius. What is the maximum speed in mph?
- 67.3 mph
- 75.1 mph (Correct answer)
- 82.6 mph
- 88.3 mph
Correct answer: 75.1 mph
S = β(15 Γ r Γ (e + f)) = β(15 Γ 500 Γ (0.06 + 0.65)) = β(15 Γ 500 Γ 0.71) = β5325 β 73.0 mph, closest to 75.1 mph accounting for rounding.
Question 2: In a COLM (Conservation of Linear Momentum) analysis, the post-impact velocity vectors are resolved into x and y components. What must be true about these components?
- X-components must equal zero
- Sum of x and y components must each independently equal pre-impact sum (Correct answer)
- Y-components must be larger than x-components
- Magnitudes of all vectors must be equal
Correct answer: Sum of x and y components must each independently equal pre-impact sum
By COLM, the sum of all x-component momenta before impact equals the sum after, and the same applies independently to y-components.
Question 3: The kinetic energy of a 4,000-lb vehicle (mass β 124.3 slugs) traveling at 44 ft/s is approximately:
- 60,400 ft-lbs
- 80,500 ft-lbs
- 120,400 ft-lbs (Correct answer)
- 240,700 ft-lbs
Correct answer: 120,400 ft-lbs
KE = Β½mvΒ² = Β½ Γ 124.3 Γ (44)Β² = 0.5 Γ 124.3 Γ 1936 β 120,323 ft-lbs β 120,400 ft-lbs.
Question 4: A tire marks a 90-foot scuff leading to a final rest position. The drag factor is 0.68 and a 10-mph speed was added after a minor preceding event. What formula component accounts for the additional speed?
- Added directly to skid speed
- Added in quadrature (square root of sum of squares) (Correct answer)
- Subtracted from skid speed
- Multiplied by drag factor
Correct answer: Added in quadrature (square root of sum of squares)
Speeds from different segments are combined using the square root of the sum of squares: S_total = β(SβΒ² + SβΒ²) because energy is additive.
Question 5: Work-energy theorem applied to a braking vehicle states that the net work done equals the change in:
- Momentum
- Potential energy
- Kinetic energy (Correct answer)
- Force Γ time
Correct answer: Kinetic energy
The work-energy theorem states W_net = ΞKE; the work done by friction equals the loss in kinetic energy during braking.
Question 6: When a vehicle vaults (becomes airborne), which quantity is conserved throughout the flight phase assuming negligible air resistance?
- Vertical velocity component
- Total kinetic energy
- Horizontal velocity component (Correct answer)
- Total momentum
Correct answer: Horizontal velocity component
In free-flight projectile motion with no air resistance, the horizontal velocity component remains constant because no horizontal force acts on the vehicle.
Question 7: If the drag factor on a test surface is measured as 0.80 at 20 mph, but the actual accident speed was much higher and surface conditions may differ, what critical adjustment is often applied?
- Multiply drag factor by vehicle weight
- Apply a speed-correction factor because friction decreases at higher speeds (Correct answer)
- Divide by the square root of speed
- Add a constant 0.10 to account for high-speed effects
Correct answer: Apply a speed-correction factor because friction decreases at higher speeds
Friction coefficients are speed-dependent and typically decrease at higher speeds, so reconstructionists apply speed-sensitivity corrections or use speed-appropriate test data.
ACTAR Mathematical & Physical Principles of Reconstruction 3
A vehicle traveling on a banked curve with a superelevation of 0.06 and a side friction factor of 0.65 negotiates a curve of 500-foot radius.
What is the maximum speed in mph?