Solve the problem.
-The motion of an object traveling along a straight path is given by $s ( t ) = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } t + s _ { 0 }$, where $s ( t )$ is the position relative to the origin at time $t$. Three observed data points are given. Find the values of $a , v _ { 0 }$, and $s _ { 0 }$.
$$s ( 1 ) = 19 , s ( 3 ) = 87 , s ( 5 ) = 171$$
A) $a = 2 , v _ { 0 } = 87 , s _ { 0 } = - 9$
B) $a = 4 , v _ { 0 } = 26 , s _ { 0 } = - 9$
C) $a = 4 , v _ { 0 } = 87 , s _ { 0 } = 171$
D) $a = 2 , v _ { 0 } = 26 , s _ { 0 } = 171$

Question

Quizplus · Accepted Answer

Substituting each data point into the equation $s(t) = \frac{1}{2}at^2 + v_0t + s_0$ and solving the system of equations yields $a = 4$, $v_0 = 26$, and $s_0 = -9$.

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