Just one more level of application of those formulae (to first approximation).
As the same equations have the same solutions, all one has to do is substitute
higher-order derivatives (and integration constants) for lower-order ones in the
equations below:
The usual formulas The jerk formulas
d -> v
v -> a
a -> k
where I've used "k" for "jerk" instead of "j" because a symbol with a dot over
it looks to me like a time-derivative.
Then, looking at acceleration, e.g.,
a = dk/dt ==> af = ai + k*t (for a constant jerk)
==> vf = vi + ai*t + 0.5*k*t^2
(note that upon "differentiating" this last, we get
af = ai + k*t, as we must).
In a sense, when we use jerk (and higher-order time-derivatives of spatial
coordinates), we're just refining the equations we normally use, but are
allowing for the possibility of applied forces (therefore, accelerations)
changing with time. The usual Taylor expansion with another term.
/**************************************
"The four points of the compass be logic, knowledge, wisdom and the unknown.
Some do bow in that final direction. Others advance upon it. To bow before the
one is to lose sight of the three. I may submit to the unknown, but never to the
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***************************************/
________________________________
From: Souder Dwight <souder.dwight@crestviewschools.net>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Thu, December 30, 2010 7:46:29 AM
Subject: [Phys-l] jerk formulas
In physics terms, I know what a jerk is, but I was curious of how it would be
shown in the typical algebraic formulas we commonly use. Can anyone show me how
the jerk would be shown in the following formulas?
vi = initial velocity
vf = final velocity
d = displacement
a = acceleration
t = time
vf = vi + (a t)
d = (vi t) + (0.5 a t^2)
vf = sqrt(vi^2 + 2 a d)