Respuesta :
Answer:
The speed is -12 when the acceleration is 0.
Explanation:
We find find the speed when the object's acceleration is 0 by using the first derivative and the second derivative of the distance equation to find the time when acceleration is 0.
[tex]\boxed{speed's\ equation = 1^{st}\ derivative\ of\ distance's\ equation}[/tex]
[tex]\displaystyle v(t)=\frac{d(t^3-6t^2-4)}{dt}[/tex]
[tex]v(t)=3(t)^{3-1}-6(2)(t)^{2-1}-0[/tex]
[tex]\bf v(t)=3t^2-12t[/tex]
[tex]\boxed{acceleration's\ equation = 2^{nd}\ derivative\ of\ distance's\ equation}[/tex]
[tex]=1^{st}\ derivative\ of\ speed's\ equation[/tex]
[tex]\displaystyle a(t)=\frac{d(3t^2-12t)}{dt}[/tex]
[tex]a(t)=3(2)t^{2-1}-12(t)^{1-1}[/tex]
[tex]\bf a(t)=6t-12[/tex]
When acceleration is 0 → a(t) = 0
[tex]a(t)=6t-12[/tex]
[tex]0 = 6t-12[/tex]
[tex]\bf t=2[/tex]
To find the speed when a(t) = 0, we substitute t = 2 to the speed's equation:
[tex]v(t)=3t^2-12t[/tex]
[tex]v(2)=3(2)^2-12(2)[/tex]
[tex]\bf=-12[/tex]
