Calculating Car Accident Speed: 100ft skid marks, 0.75g deceleration

In summary, the minimum initial speed of the car when it slammed on the brakes was 21.2 m/s or approximately 47.5 mph. This was found by using the equation vf^2 + v0^2 = 2as and solving for v0 with the given values of displacement (30.48m) and acceleration (7.35m/s^2).
  • #1
herbally
24
0

Homework Statement



Investigating the scene of a car accident you measure the skid marks of one of the cars to be 100.0ft long. Assuming that the maximum deceleration on dry pavement is 0.75g, what was the minimum speed of the car(in mph) when it slammed on the brakes?

Homework Equations



x=x0 + v0t +1/2at^2
v=v0 + at

The Attempt at a Solution



I know I need to solve for t, but I can't seem to wrap my ahead around setting up the equations for these types of problems. A helpful nudge would be appreciated.
 
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  • #2
You don't need to solve for time, you are asked to solve initial velocity. You are given 3 values, displacement, acceleration, and final velocity.
 
  • #3
I was under the impression that most of these problems begin with solving for time. I'm really in the dark on this stuff. My instructor leaves much to be desired.
 
  • #4
Have you been taught all of the basic kinematic equations?

If so, look at each of them. You'll find that each one has a different variable missing.

Knowing this all you have to do is look for the equation with all the variables you're given and the variable you need and then use that.
 
  • #5
This is what I did...let me know if I'm on the right track.

I used vf2 + v02 = 2as.

so v02 = 2(7.35m/s2)(30.48m)
v0 = 21.2m/s

I think that's right, but I'm not sure. Then of course I have to convert to mph. Am I close?
 
  • #6
Yes, that is correct.
 

1. How do you calculate the speed of a car involved in an accident?

The speed of a car involved in an accident can be calculated by using the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the deceleration, and s is the distance (in this case, the length of the skid marks). Rearranging the formula, we can get v = √(u^2 + 2as). By plugging in the values of 100ft for s and 0.75g for a (which is equivalent to 22.05 ft/s^2), we can calculate the final velocity of the car.

2. What is the significance of 100ft skid marks?

Skid marks are created when a car's tires lose traction and slide along the surface of the road. The length of the skid marks can give us an estimate of the distance the car traveled while decelerating. In this case, 100ft skid marks suggest that the car traveled 100ft before coming to a complete stop.

3. What does 0.75g deceleration mean?

Deceleration is a measure of how quickly an object is slowing down. 0.75g deceleration means that the car is slowing down at a rate of 0.75 times the acceleration due to gravity (9.8m/s^2). In other words, the car is slowing down at a rate of 22.05 ft/s^2.

4. Can the speed of a car involved in an accident be accurately calculated using only skid marks?

While skid marks can provide an estimate of the distance traveled by a car before coming to a stop, there are other factors that can affect the accuracy of the speed calculation. These factors include the type of road surface, the condition of the car's tires, and any external forces (such as a collision with another car) that may have affected the car's motion. Therefore, it is not always possible to accurately calculate the speed of a car involved in an accident using only skid marks.

5. Why is it important to calculate the speed of a car involved in an accident?

Calculating the speed of a car involved in an accident can provide important information for accident reconstruction and determining liability. It can also help determine the severity of the accident and the potential injuries sustained by those involved. Additionally, knowing the speed of the car can aid in improving road safety and preventing similar accidents in the future.

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