Dboonz

/sandbox Bewijs:
$E_{kinetisch}={\frac {1}{2}}mv^{2}$
$W={\frac {1}{2}}F*s$
$E_{kinetisch}=W$
$F=m*a$
$s=v*t\rightarrow v={\dfrac {s}{t}}$
${\frac {1}{2}}F*s={\frac {1}{2}}m*a*s={\frac {1}{2}}m*a*v*t=Ek$
${\frac {1}{2}}m*a*v*t={\frac {1}{2}}mv^{2}$
$v=a*t$
$a={\dfrac {F}{m}}$
$v={\dfrac {F*t}{m}}$
$Ek={\frac {1}{2}}m\left({\dfrac {F*t}{m}}\right)^{2}={\dfrac {1}{2}}{\dfrac {m*F^{2}*t^{2}}{m^{2}}}={\dfrac {F^{2}*t^{2}}{2m}}$

$W={\dfrac {m*a*v*t}{2}}={\dfrac {m*a*(a*t)*t}{2}}={\dfrac {m*a^{2}*t^{2}}{2}}$

$Ek={\dfrac {(m*a)^{2}*t^{2}}{2m}}={\dfrac {m^{2}*a^{2}*t^{2}}{2m}}={\dfrac {m*a^{2}*t^{2}}{2}}$
${\dfrac {m*a^{2}*t^{2}}{2}}={\dfrac {m*a^{2}*t^{2}}{2}}$