A force of 10 N acts on a body of mass 0.5 kg for 0.25s starting from rest.What is its momentum now?

Options

A. `0.25 N//s`
B. `2.5 N//s`
C. `0.5 N//s`
D. `0.75 N//s`

Answer

To find the momentum of the body after a force acts on it, we can follow these steps:

### Step 1: Understand the relationship between force, time, and momentum.
We know that the impulse experienced by an object is equal to the change in momentum. Mathematically, this can be expressed as:
\[ \text{Impulse} = F \cdot t = \Delta p \]
where \( F \) is the force applied, \( t \) is the time duration for which the force is applied, and \( \Delta p \) is the change in momentum.

### Step 2: Calculate the impulse.
Given:
- Force \( F = 10 \, \text{N} \)
- Time \( t = 0.25 \, \text{s} \)

Using the formula for impulse:
\[ \text{Impulse} = F \cdot t = 10 \, \text{N} \cdot 0.25 \, \text{s} \]
\[ \text{Impulse} = 2.5 \, \text{N} \cdot \text{s} \]

### Step 3: Relate impulse to change in momentum.
Since the body starts from rest, the initial momentum \( p_1 = 0 \). Therefore, the change in momentum \( \Delta p \) is equal to the final momentum \( p_2 \):
\[ \Delta p = p_2 - p_1 \]
\[ \Delta p = p_2 - 0 \]
\[ \Delta p = p_2 \]

### Step 4: Set the impulse equal to the change in momentum.
From the previous steps, we have:
\[ \text{Impulse} = \Delta p \]
\[ 2.5 \, \text{N} \cdot \text{s} = p_2 \]

### Step 5: Conclude the final momentum.
Thus, the final momentum \( p_2 \) of the body is:
\[ p_2 = 2.5 \, \text{N} \cdot \text{s} \]

### Final Answer:
The momentum of the body now is \( 2.5 \, \text{N} \cdot \text{s} \).

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