La trayectoria de un cuerpo en movimiento rectilíneo está determinada por: s = 115t + 12t^3 en metros y segundos. Determina la aceleración del cuerpo a los 12 segundos de origen.

Respuesta :

Answer:

a = 864 m/s^2

Step-by-step explanation:

You have the following equation for the motion of a body:

[tex]s(t)=115t+12t^3[/tex]

The acceleration of the body is given by the second derivative of s(t):

[tex]\frac{ds}{st}=115+12(3)t^2=115+36t^2\\\\\frac{d^2s}{dt^2}=\frac{d}{dt}\frac{ds}{dt}=36(2)t=72t\\\\a(t)=72t[/tex]

After t = 12 s you obtain for the acceleration:

[tex]a(t=12)=72(12)=864\frac{m}{s^2}[/tex]

hence, the acceleration is 864m/s^2 for t=12s