Question

un tren monorriel que viaja a 80km/h tiene que detenerse en una distancia de 40m ¿Que aceleración promedio requiere y cual es el tiempo de frenado?

Answer 1

$Hola~~\mathbf{Jorge} \\ \\ Datos: \\ V_0=80km/h~~--\ \textgreater \ pasemos~a~m/s=\ \textgreater \ \frac{200}{9}m/s \\ V=0 \\ S_0=0 \\ S=40m \\ a=? \\ t=? \\ \triangle _S=S-S_0=40m \\ \\ Usaremos~dos~f\acute{o}rmulas: \\ F\acute{o}rmulas \begin{cases}\boxed{V\²=V_0\²+2a \triangle _S}~----\ \textgreater \ (I) \\ \\ \boxed{V=V_0+at}~-------\ \textgreater \ (II)\end{cases}$

$Reemplazando~datos~en~la~f\acute{o}rmula~(I)~para~calcular~la~aceleraci\acute{o}n \\ tenemos: \\ 0\²=( \frac{200}{9})\²+2a(40) \\ \\ - \frac{40000}{81}=80a \\ \\ \boxed{\boxed{a=-6,17m/s\²}}~--\ \textgreater \ la~aceleraci\acute{o}n \\ \\ \mathbb{ttttttttttttttttttttttttttttttttttttttt} \\ Calculemos~el~tiempo~usando~la~f\acute{o}rmula~(II)~veamos: \\ 0= \frac{200}{9}+(-6,17)t \\ \\ - \frac{200}{9}=-6,17t \\ \\\boxed{\boxed{ t=3,6s}}~---\ \textgreater \ el~tiempo$


$\mathbb{qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Saludos!!$