# Finding Time for Instaneous Acceleration

1. Aug 17, 2007

### tonytnnt

Hi, I'm trying to figure out delta T for instantaneous acceleration.

Here's my scenario (it's not homework, I'm trying to figure out acceleration tolerance for if something gets dropped.)

If something gets dropped onto something hard, like concrete or granite, how long would it take to decelerate? Is there an equation for that or is it something I'd get out of a table? Also, is there a technical term for what I'm searching for?

2. Aug 17, 2007

### Danger

Welcome to PF, Tony.
There's no such thing as 'instantaneous' acceleration (or negative acceleration, in your case). I think that what you need are the principles for elastic or inelastic collisions. I don't know anything about that, but it comes up a lot in the Engineering section.

3. Aug 17, 2007

### pervect

Staff Emeritus
When you drop something, either the object or the floor deforms, so it doesn't stop instantly.

A good way of approximating the acceleration is to figure out what happens to the kinetic energy of the falling object. By equating the energy of the falling object to the work needed to stop it, we can write:

acceleration * distance = (1/2) * velocity^2

the left term is the amount of work done by the deaccelerating force (per unit mass), and the right term is the energy of the falling object per unit mass.

So if you know the deformation, you can find the acceleration. To find the deformation we need other equations. The simplest one would be if the object being dropped acted like an elastic spring. In that case, we can write

(1/2)*spring constant * deformation^2 = stored energy = (1/2) * mass * velocity^2

But we can't always use this formula. For instance, cars and egg cartons are designed to deliberately crumple, rather than act like springs. In this case, though, the force needed to cause the crumpling is usually known.

4. Aug 18, 2007

### tonytnnt

thanks for the info