Determine shortest distance a car could stop without causing serious injury

[cdornz]

Homework Statement

It may be assumed that the human body can withstand an acceleration of 3g's without sustaining serious injury. A person is driving a car at 60 miles per hour. Determine the shortest distance such that the car could be brought to a stop (at constant acceleration) without the driver sustaining serious injury.

Homework Equations

Ag's = a/g
d = (V_i + V_f)/2 * t (d stands for displacement)

The Attempt at a Solution

I converted the 3g's into an acceleration so I at least have a comparable number when I try and get the answer. 3*32ft/s² = 96ft/s²

I haven't done this type of problem in quite a few months, so I forget where to start per say. I did convert the 60 miles per hour to feet per second, 88ft/s. I don't remember if the equation I listed above is the right one to use in this situation, especially since I don't know time or the displacement.

 

[TSny]

If you are initially traveling at 88 ft/s, how much time will it take to come to rest if you are decelerating at 96 ft/s per second?

Then you can use your distance formula.

(There are also other formulas for constant acceleration. There's a formula that will give you the distance directly from the initial and final velocities and the acceleration without needing the time.)

 

[ap123]

You need to use an equation that doesn't involve time.
You can use
v^2 = u^2 + 2as

 

[cdornz]

thank you! I figured I had the information I needed, I just wasn't sure about the equation necessary to find the solution.

 

[Nickie]

I would approach this problem by first defining the variables and units involved. The given acceleration of 3g's can be converted to 96 ft/s2, as you have correctly done. The initial velocity (Vi) is 88 ft/s, and the final velocity (Vf) is 0 ft/s (since the car needs to come to a complete stop). The time (t) and displacement (d) are the unknown variables we need to solve for.

Next, I would use the kinematic equation d = (Vi + Vf)/2 * t to solve for the displacement. Since we know the initial and final velocities, we can plug those values in and solve for t. This will give us the time it takes for the car to come to a stop.

Once we have t, we can plug that value back into the equation to solve for d, which will give us the shortest distance the car can stop without causing serious injury. It is important to note that this distance will vary depending on the deceleration rate of the car, which can be affected by factors such as road conditions, tire traction, and braking system efficiency.

In conclusion, as a scientist, I would use mathematical equations and principles to solve for the shortest distance a car can stop without causing serious injury. However, it is important to keep in mind that there are many variables and factors that can affect this distance in real-life situations.