Question

1. the distance a freely falling object falls is modeled by the formula ( d = 16t^{2} ), where ( d ) is the distance in feet that the object falls and ( t ) is the time elapsed in seconds.

2a complete the table.

2b when ( t = 0 ), we get ( d = 0 ).
what does this mean?
a ( t = 0 ) is the time when the object lands on the ground.
b when the object hits the ground, time stops.
c the object is initially at ground level.
d initially, the object has not traveled any distance.

Explanation:

• Option A: When \(t = 0\), the object has just started falling, not landed. So this is incorrect.
• Option B: Time does not stop when the object hits the ground. The formula \(d = 16t^{2}\) is just a model for the falling distance as a function of time. So this is incorrect.
• Option C: The formula \(d = 16t^{2}\) gives the distance the object has fallen. If \(d = 0\) at \(t=0\), it means no distance has been traveled, not that it is at ground - level (it could be at some initial height before starting to fall). So this is incorrect.
• Option D: Since \(d\) represents the distance fallen and \(d = 16t^{2}\), when \(t = 0\), \(d=0\) implies initially, the object has not traveled any distance.

Answer:

D. Initially, the object has not traveled any distance.