An object moving vertically is at the given heights at the specified times. find the position equation
s = 1/2 at^2 + v 'subtext o' t 'subtext o' + s 'subtext o' for the object
at t=1 seconds, s= 161 ft
at t=2 seconds, s= 98 ft
at t=3 seconds, s= 3 ft
a. s= -8t^2 - t - 192
b. s= -32t^2 - 15t + 161
c. s= -16t^2 + 15t + 161
d. s= -16t^2 - 15t - 192
e. s= -16t^2 - 15t + 192
+33653 You can see immediately that neither a nor d can be correct as they give negative heights for all values of t, whereas the question specifies positive heights.
You can also rule out b because this could only give a height of 161 at time t = 0, and for greater times, including t= 1, the height would be less than 161, which would conflict with the information given in the question.
Substitute one of the given times into c and e to see which produces the corresponding specified height.
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