To determine the correct equation that can be used to calculate the time of impact (∆t) when given the impulse (I) and the force (F) applied to an object, we start with the fundamental relationship between impulse, force, and time.
Impulse (I) is defined as the product of the force (F) applied to an object and the time duration (∆t) over which the force is applied. Mathematically, this relationship is given by:
[tex]\[
I = F \Delta t
\][/tex]
To find the time of impact (∆t), we need to solve for ∆t in terms of I and F. We can rearrange the equation by isolating ∆t:
[tex]\[
\Delta t = \frac{I}{F}
\][/tex]
Thus, the correct equation to calculate the time of impact when you have the impulse (I) and the force (F) applied to an object is:
[tex]\[
\Delta t = \frac{I}{F}
\][/tex]
Now, let's review the options provided and identify the correct one:
A. [tex]\(\Delta t = \frac{F}{I}\)[/tex]
B. [tex]\(\Delta t = \frac{1}{F}\)[/tex]
C. [tex]\(\Delta t = FI\)[/tex]
D. [tex]\(\Delta t = \frac{1}{IF}\)[/tex]
From the options, we see that the correct equation:
[tex]\(\Delta t = \frac{I}{F}\)[/tex]
corresponds to:
E. None of the above. (This is NOT an option.)
Therefore, the answer must be [tex]\(\Delta t = \frac{I}{F}\)[/tex], which corresponds to option A.
Hence, the correct choice is:
[tex]\[
\boxed{1}
\][/tex]
