Physics Course/Motion/Non - Linear Motion

Motion not in straight line like Curve motion

Characteristics of Curve Motion

Average acceleration

$a={\frac {\Delta v(t)}{\Delta t}}={\frac {v(t+\Delta t)-v(t)}{(t+\Delta t)-t}}$

Aerage speed

$s=\Delta t[v(t)+{\frac {\Delta v(t)}{2}}]$

Instantenous acceleration

$a(t)={\frac {d}{dt}}v(t)={\frac {v(t+\Delta t)-v(t)}{(t+\Delta t)-t}}$

Instantenous speed

$s(t)=\int v(t)dt$

Formual of Curve motion

Characteristics	Symbol	Calculus Equation
Speed	v	$v(t)$	${\frac {d}{dt}}s(t)$
Accelleration	a	${\frac {d}{dt}}v(t)$	${\frac {d^{2}}{dt^{2}}}s(t)$
Distance	s	$\int v(t)dt$	$s(t)$
Force	F	$m{\frac {d}{dt}}v(t)$	$m{\frac {d^{2}}{dt^{2}}}s(t)$
Work	W	$F\int v(t)dt$	p ${\frac {d}{dt}}s(t)$
Energy	E	${\frac {F}{t}}\int v(t)dt$	p ${\frac {d^{2}}{dt^{2}}}s(t)$