User:Dboonz

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

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

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