# What a jerk!

Ja4Coltrane
I want to know if there is any real physical situation where there is a constant jerk (third derivative of displacement with respect to time). I am perfectly aware of how common jerk is as well as countless higher derivatives. I actually want to know if there is something as simple as a constant force causing a constant acceleration. In other words, is there any physical situation where a force increases constantly and linearly over some non infinitesimal time interval?

Homework Helper
If you stretch a spring at a constant rate (dx/dt= constant), the force, F= kx, increases linearly at a constant rate.

Ja4Coltrane
well, that's not what I mean, I don't mean linearly with the variable of displacement, I mean time.

Ja4Coltrane
oh,I see
sorry

Ja4Coltrane
but that does not work, I need net force.
in other words, I only care whether or not a constant jerk can exist.

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Staff Emeritus
Gold Member
I actually want to know if there is something as simple as a constant force causing a constant acceleration. In other words, is there any physical situation where a force increases constantly and linearly over some non infinitesimal time interval?

Your "in other words" is a complete rewording of what came before it! On the one hand, you want to know about constant forces, and on the other hand you want to know about constantly increasing forces. Which is it? No matter, both can be addressed. But do keep in mind that they are different!

An instance of a constant force causing a constant acceleration happens whenever a constant force acts on a particle. In that case, Newton's 2nd law says that $\vec{F}=m\vec{a}$. In words that implies that the force is proportional to the acceleration. When one is constant, so is the other.

The example of Hooke's law provided above gives you an example of the second thing you asked for, which once again is not the same as the first.

Ja4Coltrane
edit: deleting this...

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Ja4Coltrane
hold on
1) what is this second and what is this first, I didnt mean to ask anything about constant forces.
2) I did not mean that I just want an example of constantly changing force--I want an example of constantly changing net force. The hooke's law example does not do that.

do you see what I am saying?

Staff Emeritus
Gold Member
well, that's not what I mean, I don't mean linearly with the variable of displacement, I mean time.

If you mean linearly with respect to time, then this can be rigged up with an appropriate machine. As a first approximation, consider a mass on a frictionless surface. Let a cord be attached to the mass and drawn over a pulley. Let the other end of the pulley be attached to a pan, into which flows a steady stream of water. The weight in the pan (and therefore, the horizontal force on the car) will grow linearly in time.

Ja4Coltrane
hehe, I like that example thanks.
it is rigged, but it's cool.
thanks.

Ja4Coltrane