If force F=500-100t, then function of impulse with time will be,-

Options

A. `500t-50t^(2)`
B. 50t – 10
C. `50 – t_(2)`
D. `100t^(2)`

Explanation

To find the function of impulse with time given the force \( F = 500 - 100t \), we can follow these steps:

### Step 1: Understand the relationship between force and impulse
Impulse is defined as the change in momentum, which can also be expressed as the integral of force over time:
\[ \text{Impulse} = \int F \, dt \]

### Step 2: Substitute the given force into the impulse formula
Given the force \( F = 500 - 100t \), we substitute this into the impulse formula:
\[ \text{Impulse} = \int (500 - 100t) \, dt \]

### Step 3: Integrate the force function
Now we will perform the integration:
\[ \text{Impulse} = \int (500 - 100t) \, dt = \int 500 \, dt - \int 100t \, dt \]

Calculating each integral separately:
1. \(\int 500 \, dt = 500t\)
2. \(\int 100t \, dt = 50t^2\) (using the power rule of integration)

Combining these results, we have:
\[ \text{Impulse} = 500t - 50t^2 + C \]
where \( C \) is the constant of integration.

### Step 4: Write the final expression for impulse
Since we are looking for the function of impulse with respect to time, we can ignore the constant \( C \) for this context. Thus, the function of impulse with time is:
\[ \text{Impulse}(t) = 500t - 50t^2 \]

### Final Answer
The function of impulse with time is:
\[ \text{Impulse}(t) = 500t - 50t^2 \]

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