NTN Police Police Work Mathematics 2 — Questions and Answers

Question 1: Skid marks at a collision scene measure 120 feet. Using the skid mark formula S = √(30 × d × f) where f = 0.70 (friction coefficient for a wet road), what is the approximate pre-braking speed of the vehicle?

50 mph
45 mph (Correct answer)
60 mph
35 mph

Correct answer: 45 mph

S = √(30 × 120 × 0.70) = √(2520) ≈ 50.2 mph, so approximately 50 mph.

S = √(30 × 120 × 0.70) = √(2520) ≈ 50.2 mph. The friction coefficient of 0.70 reflects a wet road surface, which provides less traction than dry asphalt (typically 0.75–0.85). A lower friction coefficient means longer skid marks for the same speed — vehicles take longer to stop on wet roads. Traffic accident reconstruction specialists use this formula along with scene measurements to calculate speed and determine if a driver was traveling above the speed limit at the time of braking.

Question 2: An officer works a 10-hour shift. They spend 35% of the shift on patrol, 25% on calls, 20% on report writing, and 10% on court time. How many hours are spent on patrol?

3 hours
3.5 hours (Correct answer)
4 hours
2.5 hours

Correct answer: 3.5 hours

35% of 10 hours = 0.35 × 10 = 3.5 hours on patrol.

To find the time spent on patrol: 35% × 10 hours = 0.35 × 10 = 3.5 hours. This type of calculation is used in departmental time management and workload analysis. Officers must understand shift time distribution for scheduling, overtime calculation, and resource allocation. Note that the percentages listed (35 + 25 + 20 + 10 = 90%) account for 9 hours, leaving 1 hour for other activities.

Question 3: A department has a 1:500 officer-to-resident ratio goal. If a city has 125,000 residents, how many officers does the department need to meet this goal?

200
250 (Correct answer)
225
275

Correct answer: 250

125,000 ÷ 500 = 250 officers needed to meet the 1:500 ratio.

To find the required number of officers: 125,000 residents ÷ 500 (ratio) = 250 officers. Officer-to-population ratios are a standard metric for police staffing decisions. The FBI has traditionally used staffing benchmarks in its Uniform Crime Report data, though recommended ratios vary by community type, crime rate, and geography. Understanding this calculation is useful for budget justifications, grant applications, and resource planning.

Question 4: Officers are distributing patrol hours across three precincts based on call volume. Precinct A handles 40% of calls, Precinct B handles 35%, and Precinct C handles 25%. If the department allocates 2,000 patrol hours per month, how many hours go to Precinct B?

700 hours (Correct answer)
800 hours
900 hours
500 hours

Correct answer: 700 hours

35% of 2,000 = 0.35 × 2,000 = 700 hours allocated to Precinct B.

Precinct B's allocation: 35% × 2,000 hours = 0.35 × 2,000 = 700 hours. This type of proportional allocation based on call volume or population is standard in police resource management. Verifying: Precinct A = 40% × 2,000 = 800 hours, Precinct B = 700 hours, Precinct C = 500 hours. Total = 800 + 700 + 500 = 2,000 hours. Officers in supervisory and administrative roles regularly perform these calculations for budget and scheduling purposes.

Question 5: An officer drives 12 miles to a call at an average speed of 48 mph (with emergency lights). How many minutes does the response take?

12 minutes
15 minutes (Correct answer)
18 minutes
10 minutes

Correct answer: 15 minutes

Time = Distance ÷ Speed = 12 ÷ 48 = 0.25 hours = 0.25 × 60 = 15 minutes.

Time = Distance ÷ Speed = 12 miles ÷ 48 mph = 0.25 hours. To convert to minutes: 0.25 hours × 60 minutes/hour = 15 minutes. Officers and dispatchers use this type of calculation to estimate response times, prioritize calls, and plan multi-unit responses to ensure coverage. Response time is also a key performance metric tracked by departments and evaluated in after-action reviews.

Question 6: A department seized 3.5 pounds of marijuana during a search. There are 453.6 grams in one pound. Approximately how many grams of marijuana were seized?

1,350 grams
1,588 grams (Correct answer)
1,200 grams
1,750 grams

Correct answer: 1,588 grams

3.5 × 453.6 = 1,587.6 grams, which rounds to approximately 1,588 grams.

3.5 lbs × 453.6 g/lb = 1,587.6 grams ≈ 1,588 grams. Drug weight conversions between imperial and metric units are essential in law enforcement because statutes specify drug quantities in grams (metric system). Officers must accurately convert between units when recording seized quantities for charging decisions, evidence documentation, and NCIC entries. The gram is the standard unit for controlled substance weight in U.S. drug statutes, while field measurements may initially be in pounds and ounces.

NTN Police Police Work Mathematics 2

Skid marks at a collision scene measure 120 feet.
Using the skid mark formula S = √(30 × d × f) where f = 0.70 (friction coefficient for a wet road), what is the approximate pre-braking speed of the vehicle?