Is it possible to have a system that has constant jerk? Example?

Question

I was on my drive home the other day and somehow started to think about this. I know you can achieve constant accelleration, but somehow a system with constant jerk seems just out of my perception. I mean...the velocity would be increasing exponentially. And that seems a bit far fetched to me. What could possibly have so much thrust that it's velocity increases exponentially? I thought maybe a just-fired bullet, but that would be for only microseconds before drag, friction, and gravity all factored in.

Answer 1

"Jerk" simply means change in acceleration. So all we would need is something that has a constant change of acceleration.

An example might be a rocket that constantly increases the amount of fuel that it uses, such that its acceleration would increase linearly, which is equivalent to constant jerk.

Another example might be to imagine that the Earth's gravity increased at a linear rate (since gravity is the same as acceleration). You would feel yourself getting constantly heavier.

Answer 2

For the confused sorts above me, "jerk" is the seldom used but still official term for the third time derivative of position, or change in acceleration over time.

Just as acceleration can only be non-zero constant for so long, same with jerk. Any system you come up with will eventually have to change jerk or run wild.

Here's a nice simple mechanical example of constant jerk. Take rope and wind it around a cone, then connect the end of the rope to a mass. As the mass drops, the lever arm changes, which changes the torque and therefore the acceleration.

Torque = Fr.

F is the tension in the cord, mg - T = ma, so torque = mr(g-a).

Torque = I alpha, where I is constant and alpha is the angular acceleration of the cone. alpha is a/r if we assume no slip. So Ia/r = mr(g-a), solving for a gives us:

a = mgr(mr+I/r) = m^2gr^2 + mgI

da/dt = 2m^2gr dr/dt

So, for some shape of cone, r dr/dt can be constant. Okay, not as simple as I thought, we're probably looking at something weird like a catenaroid or whatever. Might not be solveable, it's been a long time since DiffEq for me. :)

Answer 3

http://s223.photobucket.com/albums/dd78/floodtl/?action=view¤t=constantjerk.jpg

Here's an illistration of the rocket described in tastywheat's answer. It burns fuel at a linearly increasing rate. I know that's not how solid fuel works but it's just to get the idea across.

Answer 4

Jerk??
I've taken a lot of Physics classes, but I've never heard of 'jerk'. Impulse, yes. But never 'jerk' ☺

Doug

Answer 5

yes, ever watch best damn sports show period? Tom Arnold is your answer! constant jerk!