Solve the Problem $s ( t ) = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } t + s _ { 0 }$

Multiple Choice

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) $a = 2 , v _ { 0 } = 26 , s _ { 0 } = 171$