Law Enforcement Mathematics Flashcards

An officer on patrol is driving at 65 mph. A car passes the officer going in the same direction at a constant speed. The officer uses a roadside marker to determine the car is pulling away at a rate of 15 mph. Which of the following equations correctly represents the speed of the other car (C)?

Answer: C = 65 + 15

Since the car is pulling away from the officer while traveling in the same direction, its speed is the sum of the officer's speed and the rate at which it's pulling away. Therefore, you add the officer's speed (65 mph) to the separation speed (15 mph) to find the car's total speed. 65 + 15 = 80 mph.

An investigator is sketching a crime scene in a rectangular room that is 25 feet long and 18 feet wide. A piece of evidence is located by taking two measurements from one of the corners. The first measurement is 8 feet along the length of the room, and the second is 5 feet along the width. What is the total area of the room?

Answer: 450 square feet

The area of a rectangle is calculated by multiplying its length by its width. The location of the evidence is extra information not needed to solve the problem. Area = Length × Width. Area = 25 ft × 18 ft = 450 square feet.

An officer responds to an accident scene and measures a single, continuous skid mark of 120 feet on a dry asphalt road. Using the common formula S = √(30 * f * d), where S is speed in mph, 'f' is the drag factor, and 'd' is the skid distance in feet, what was the vehicle's minimum initial speed if the drag factor ('f') for dry asphalt is 0.7?

Answer: ~50.2 mph

Substitute the given values into the formula: S = √(30 * 0.7 * 120). First, multiply the numbers inside the square root: 30 * 0.7 * 120 = 2520. Then, find the square root of 2520, which is approximately 50.2. So, S ≈ 50.2 mph.

Officer A and Officer B start from the same police station at the same time, heading in opposite directions on a straight highway. Officer A travels at 55 mph, and Officer B travels at 60 mph. How much time will have passed when they are 230 miles apart?

Answer: 2.0 hours

Because the officers are traveling in opposite directions, their speeds combine. The combined speed is 55 mph + 60 mph = 115 mph. To find the time it takes to be 230 miles apart, use the formula Time = Distance / Speed. Time = 230 miles / 115 mph = 2 hours.

An officer collects 48 items of evidence from a large crime scene. If 3/4 of the items are fingerprints and the rest are other forms of trace evidence, how many items are NOT fingerprints?

Answer: 12

First, find the number of fingerprint items: 48 * (3/4) = 36. To find the number of items that are not fingerprints, subtract this from the total: 48 - 36 = 12. Alternatively, if 3/4 are fingerprints, then 1/4 are not. 48 * (1/4) = 12.

An officer drives a patrol route that is 32 miles long. If the officer completes the entire route in 45 minutes, what is their average speed in miles per hour (mph)?

Answer: 43 mph

First, convert the time from minutes to hours by dividing by 60: 45 minutes / 60 = 0.75 hours. Then, use the formula Speed = Distance / Time. Speed = 32 miles / 0.75 hours = 42.66... mph. The closest answer is 43 mph.