Question

this step clearly shows that the force needed to stop an object is _directly_ (directly/inversely) proportional to the amount of time needed to stop an object. according to the impulse - change in momentum theorem, an object with 100 units of momentum must experience 100 units of impulse in order to be brought to a stop. any combination of force and time could be used to produce the 100 units of impulse necessary to stop an object with 100 units of momentum. this is depicted in the table below.

combinations of force and time required to produce 100 units of impulse
100	1	100
50	2	100
25	4	100
10		100
4		100
2		100
1		100
0.1		100

Explanation:

Step1: Recall the impulse formula

The impulse \( J \) is given by the product of force \( F \) and time \( t \), so \( J = F \times t \). Here, \( J = 100 \) units (constant for stopping the object).

Step2: Solve for time when force is 10

Given \( F = 10 \) and \( J = 100 \), use \( t=\frac{J}{F} \). Substitute values: \( t=\frac{100}{10}=10 \).

Step3: Solve for time when force is 4

For \( F = 4 \), \( t=\frac{100}{4}=25 \).

Step4: Solve for time when force is 2

For \( F = 2 \), \( t=\frac{100}{2}=50 \).

Step5: Solve for time when force is 1

For \( F = 1 \), \( t=\frac{100}{1}=100 \).

Step6: Solve for time when force is 0.1

For \( F = 0.1 \), \( t=\frac{100}{0.1}=1000 \).

Answer:

For Force = 10, Time = 10;
For Force = 4, Time = 25;
For Force = 2, Time = 50;
For Force = 1, Time = 100;
For Force = 0.1, Time = 1000.