# Was the Speed Calculation Correct for Fighting the Ticket?

• umdece4
In summary: Keep up the good work!In summary, based on the given information, the speed at which you slammed on your brakes was approximately 36 mph. It is recommended to seek legal advice and present these calculations in court to determine if fighting the traffic ticket is justified.
umdece4

## Homework Statement

You are driving your car uphill along a straight road. Suddenly, you see a car run a red light and enter the intersection just ahead of you. You slam on your brakes and skid in a straight line to a stop, leaving skid marks 116 feet long. A policeman observes the whole incident and gives a ticket for exceeding the speed limit of 45 mph. When you get home, you read your physics textbook and estimate that the coefficient of kinetic friction between your tires and the road is 0.5, and the coefficient of static friction is 0.80. You go back and measure the angle that the hill makes with the horizontal and find it to be 6 degrees. You look in your owners manual and find that the car weighs 1820 lbs. Find the speed (in MPH) at the instant that you slammed the brakes and determine for yourself if you should fight the traffic ticket in court.

## The Attempt at a Solution

I don't remember exactly what i did but i could not get the right answer. it ranged between 22.87 mph to 50.95 mph.

Firstly, I would like to commend you for taking the time to consider the physics behind this incident and attempting to calculate the speed at which you slammed on your brakes. it is important to use critical thinking and evidence-based analysis in situations like these.

Based on the information provided, here is my attempt at a solution:

1. We can use the formula for kinetic friction (Fk = μk * N) to calculate the force of kinetic friction acting on your car during the skid. N is the normal force and can be calculated using the weight of the car (1820 lbs) and the angle of the hill (6 degrees). N = 1820 lbs * cos(6) = 1815.95 lbs. Converting this to Newtons, we get N = 8091.31 N.

2. Next, we can use the formula for acceleration (a = F/m) to calculate the deceleration (a) of your car during the skid. F is the force of kinetic friction calculated in step 1, and m is the mass of the car in kg. Converting 1820 lbs to kg, we get m = 826.73 kg. Plugging in the values, we get a = 8091.31 N / 826.73 kg = 9.78 m/s^2.

3. Since the skid marks were 116 feet long, we can use the formula for distance (d = v^2/2a) to calculate the initial velocity (v) of your car before slamming on the brakes. d is the skid distance (116 feet or 35.36 meters), and a is the deceleration calculated in step 2. Plugging in the values, we get v = √(2 * 9.78 m/s^2 * 35.36 m) = 16.06 m/s = 36 mph.

Therefore, based on these calculations, it seems that you were traveling at a speed of 36 mph when you slammed on your brakes. This is above the speed limit of 45 mph, so it is possible that the ticket was justified. However, it is important to consider other factors such as reaction time and the possibility of the other driver being at fault. It would be best to consult with a lawyer and present these calculations as evidence in court.

I hope this helps and encourages you to

## 1. How is speed calculated from a skidding stop?

Speed from a skidding stop is calculated using the formula: Speed = Square root of (friction coefficient x acceleration due to gravity x skid distance).

## 2. What is a friction coefficient?

A friction coefficient is a measurement of the resistance to motion between two surfaces in contact. It is represented by the symbol "μ" and varies depending on the materials and conditions of the surfaces.

## 3. Why is acceleration due to gravity a factor in calculating speed from a skidding stop?

Acceleration due to gravity, denoted by the symbol "g", is a constant value that represents the rate at which objects fall towards the Earth. It plays a role in calculating speed from a skidding stop because it affects the amount of force needed to overcome the friction between the tires and the road surface.

## 4. How does skid distance impact the calculation of speed from a skidding stop?

Skid distance is the distance traveled by a vehicle while its tires are locked and sliding on the road surface. It is an important factor in the calculation of speed from a skidding stop because it directly affects the amount of time it takes for a vehicle to come to a complete stop.

## 5. Can speed from a skidding stop be used to determine the speed of a moving vehicle?

No, speed from a skidding stop can only be used to determine the speed at which a vehicle was traveling before coming to a stop. It cannot be used to determine the speed of a moving vehicle because it does not take into account other factors such as acceleration or deceleration during the skid.

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