The rule below shows how to find the position of an object thrown upward with initial velocity of 15 feet per second. which answer expresses that rule in the form of an equation? square the input and then multiply it by -16. add this product to the initial velocity multiplied by the input. a. f(t) = 16t2 + 15t2 b. f(t) = (-16t+ 15t)2 c. f(t) = 16t2 - 15t d. f(t) = -16t2 + 15t

Here we're applying a basic physics rule for vertical motion where the only pull on the object is gravity.

This rule has the form

h(t) = h + v t + (1/2)a*t^2

o o

To adapt this rule to this particular question replace h with 0, as the

o

upward path of the object begins at 0 ft. Replace v with +15 ft/sec.

o

Replace "a" with (-32.2 ft/(sec^2); this is the acceleration due to gravity.

Then we have the following, with the label F(t):

F(t) = 0 + (15 ft/sec)t + (1/2)(-32.2 ft)/(sec^2), or

F(t) = 15t - 16.1t^2. Thus, Choice D is correct.

Please note: To avoid confusion, please use " ^ " to denote exponentiation:

F(t) = -16t^2 + 15t