Deceleration without knowing the time

[BOAS]

Homework Statement

What net force would be necessary to stop an automobile of mass 1000kg traveling initially at a speed of 15m/s in a distance equal to the diameter of a dime, which is 1.8cm ?

Homework Equations

The Attempt at a Solution

The force required to stop the car is given by F = dp/dt.

Change in momentum = mv - mv₀

As far as I can see, it's not possible for me to determine a time in which this change in momentum takes place. I have been staring at it for ages and not making any head way.

Thanks for any help you can give.

 

[DrClaude]

You have to introduce distance. What is the relationship between acceleration and distance travelled?

 

[BOAS]

Acceleration is the second derivative of displacement with respect to time.

 

[mfb]

Acceleration is the second derivative of displacement with respect to time.

That is correct, but not the important point.

There are two approaches:
(a) assuming constant deceleration, what is the relationship between initial velocity, acceleration and distance traveled in the stopping process?
(b) Work with the energy of the car.

 

[BOAS]

I was overcomplicating this... a = (v^2 - u^2)/2s

I have solved the problem.

 

[BOAS]

That is correct, but not the important point.

There are two approaches:
(a) assuming constant deceleration, what is the relationship between initial velocity, acceleration and distance traveled in the stopping process?
(b) Work with the energy of the car.

I just realized my mistake before reading your post. I moved on to the next problem and the answer to this one was staring me in the face.