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
