# 태권도 물리: Lesson 5 – Jerk!

In martial arts, perhaps it pays to be a jerk! In kinematics, jerk is defined as the change in acceleration over time. Jerk or jolt is useful in designing roller coasters for the maximum, well, jolt in order to give the rider the best bang for the buck in terms of roller coaster rides. Jerk with respect to force is shown by:

$j=\frac{dF}{mdt}$.

Recall Newton’s Second Law$F_{kick}=ma$. If a martial artist lacks mass, s/he must have acceleration. A more accurate way of stating this is $F_{arm}=\frac{d\rho}{dt}$. This implies that a martial artist must master momentum and time, but we can also relate force and mass to the desired jolt that we want to impart on an opponent, say with a kick or punch. In this case, it pays to have less mass and to be fast, for mass and dt are inversely related to the change in force and the jerk. In other words, if you are faster and smaller, you can be a bigger jerk!

In Lesson 4 we figured out that a 45 kg (100 lb) martial artist could impart 478.8 N of force through his/her 10 kg fist or foot traveling 0.3 m at 4 m/s. Plugging this in we get a jerk of about $j=\frac{d478.8}{45d0.075}=141.9\frac{m}{s^3}$ or 14.4 g/s. Note that it only takes about 10 g/s to cause a concussion!

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