Question

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.

Answer 1

a = 864 m/s^2

Explanation:

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

`s(t)=115t+12t^3`

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

`(ds)/(st)=115+12(3)t^2=115+36t^2\\\\(d^2s)/(dt^2)=(d)/(dt)(ds)/(dt)=36(2)t=72t\\\\a(t)=72t`

After t = 12 s you obtain for the acceleration:

`a(t=12)=72(12)=864(m)/(s^2)`

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