Why Does Stopping Distance Increase with Speed?

[Bashyboy]

In my physics textbook, it states that the stopping distance increases with the square of the intial speed. Could someone provide me with an example of why this is true?

Thank you

 

[Doc Al]

For constant acceleration, how does distance relate to speed? (Look for a connecting kinematic formula.)

 

[Bashyboy]

Would it be the kinematic equation v^2 = vi^2 + 2a(x - xi) solved for delta x?

 

[Doc Al]

Would it be the kinematic equation v^2 = vi^2 + 2a(x - xi) solved for delta x?

Exactly. Vi would be the initial speed; V = 0, the final speed.