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The velocity, in ft/sec of a particle is given by v(t) =-14t + 2. Find the position function s(t) of the particle if it has an initial position s(0) = 4 feet.

The velocity in ftsec of a particle is given by vt 14t 2 Find the position function st of the particle if it has an initial position s0 4 feet class=

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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

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