Mathematical & Physical Principles of Reconstruction Flashcards

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?

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.

The principle of the coefficient of friction is that frictional force is independent of:

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.

A vehicle decelerates at 0.85 g from 55 mph. Approximately how far does it travel before stopping (1 g = 32.2 ft/s²)?

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.

Which statement best describes the difference between 'speed' and 'velocity' in crash reconstruction?

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.

During a vault (airborne) phase, a vehicle's horizontal range R is determined by which variables?

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.

Newton's Third Law, as applied to crash reconstruction, implies that during a collision:

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.

The term 'minimum speed' in skid analysis refers to a speed that is considered conservative because:

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.