Answer:
Option B is correct
[tex]s(t)=-7t^{2}+2t+4[/tex]
Explanations;
Given the velocity of the particle expressed as;
[tex]v(t)=-14t+2[/tex]
The position of the object is determined by integrating the velocity function as shown:
[tex]\begin{gathered} s(t)=\int v(t)dt \\ s(t)=\int(-14t+2)dt \\ s(t)=-\frac{14t^2}{2}+2t_+C \\ s(t)=-7t^2+2t+C \end{gathered}[/tex]
If the particle has an initial position s(0) = 4 feet, then;
[tex]\begin{gathered} s(0)=-7(0)^2+2(0)+C \\ 4=C \end{gathered}[/tex]
Substitute the constant into the position function to have:
[tex]s(t)=-7t^2+2t+4[/tex]
This gives the required position of the particle
