# Physics Course/Non Linear Motion

## Non Linear Motion

Non Linear Motion refers to any non straight line motion with changing direction

## Characteristics

For any Non Linear Motion can be represented mathematically as a function of speed in time, v(t) then

• Speed
v = v(t)
• Accelleration
${\displaystyle a={\frac {dv(t)}{dt}}}$
• Distance
${\displaystyle s=\int v(t)dt}$
• Force
${\displaystyle F=m{\frac {dv(t)}{dt}}}$
• Work Done
${\displaystyle W=F\times s=F\int v(t)dt}$
• Energy
${\displaystyle W={\frac {F}{t}}={\frac {F}{t}}\int v(t)dt}$

## Summary

Characteristics Symbol Calculus Equation
Speed v ${\displaystyle {\frac {ds(t)}{dt}}}$
Accelleration a ${\displaystyle {\frac {dv(t)}{dt}}={\frac {d^{2}s}{dt^{2}}}}$
Distance s ${\displaystyle \int v(t)dt}$
Force F ${\displaystyle m{\frac {dv(t)}{dt}}}$
Work W ${\displaystyle {\frac {F}{t}}\int v(t)dt}$
Pressure P ${\displaystyle {\frac {ds(t)}{dt}}}$
Impulse Fm ${\displaystyle mt{\frac {dv(t)}{dt}}}$
Momentum mv ${\displaystyle m{\frac {ds(t)}{dt}}}$
Energy E ${\displaystyle F\int v(t)dt}$