# C1 continuity

1. Sep 30, 2008

### 12monkey

Dear all,
I would appreciate if you could help me with the following problem:
A person is standing still on a 2D environment and let's assume that its initial position Xo is given. The person is moving by applying a force function over time say f(t). As a result, using numerical integration we can determine the person's acceleration, velocity and position at any time step.
My question is how we can prove that the resulting path/motion is or is not C1 continuous?

2. Sep 30, 2008

### mathman

As long as f(t) is finite, the resultant velocity will be continuous.

3. Sep 30, 2008

### HallsofIvy

Staff Emeritus
F= ma and v is the integral of a. That is, v is the integral of f(t)/m. As long as the set of points at which the function f(t) is discontinuous has measure 0 (no more that countably infinite is sufficient) and those discontinuities are step discontinuities (and if, as mathman says, the function is finite that is true) then its integral is continuous.