Question

Graph the function.How far has the artifact fallen from time t=0 to t= 1?

Answer 1

The height h (in feet) for a free-fall artifact is given by:

`h(t)=-16t^2+98`

Part A:

The graph of the function is:

Part B:

To find the distance traveled from t = 0 to t = 1, we perform the subtraction:

`\Delta^(0,1)_h=|h(0)-h(1)|`

Now, evaluating the function for t = 0 and t = 1:

`\begin{gathered} h(0)=-16\cdot0^2+98=98 \\ h(1)=-16\cdot1^2+98=82 \end{gathered}`

Then:

`\Delta^(0,1)_h=|98-82|=16`

The artifact traveled 16 feet from t = 0 to t = 1.

Part C:

h(t) is a quadratic function (non-linear), so we can conclude that the distance traveled from t = 1 to t = 2 is not the same as from t = 0 to t = 1.

To confirm this, we calculate the first distance. Evaluating the function for t = 2:

`h(2)=-16\cdot2^2+98=34`

Now, the distance traveled from t = 1 to t = 2 is:

`\Delta^(1,2)_h=|h(1)-h(2)|=|82-34|=48`

Which is different from the distance in part B (16 feet).