To solve the problem step by step, we will follow the principles of impulse and momentum.
### Step 1: Calculate the Impulse
Impulse (J) is defined as the product of the force (F) applied and the time interval (Δt) over which it is applied. The formula for impulse is given by:
\[ J = F \times \Delta t \]
Given:
- Force, \( F = 5 \, \text{N} \)
- Time interval, \( \Delta t = 2 \, \text{milliseconds} = 2 \times 10^{-3} \, \text{s} \)
Substituting the values into the formula:
\[ J = 5 \, \text{N} \times (2 \times 10^{-3} \, \text{s}) \]
Calculating:
\[ J = 10 \times 10^{-3} \, \text{N s} = 10^{-2} \, \text{N s} \]
### Step 2: Relate Impulse to Change in Velocity
Impulse is also related to the change in momentum, which can be expressed as:
\[ J = m \times \Delta v \]
Where:
- \( m \) is the mass of the body
- \( \Delta v \) is the change in velocity
Given:
- Mass, \( m = 5 \, \text{g} = 5 \times 10^{-3} \, \text{kg} \)
We can set the impulse equal to the mass times the change in velocity:
\[ 10^{-2} \, \text{N s} = (5 \times 10^{-3} \, \text{kg}) \times \Delta v \]
### Step 3: Solve for Change in Velocity
Rearranging the equation to solve for \( \Delta v \):
\[ \Delta v = \frac{10^{-2} \, \text{N s}}{5 \times 10^{-3} \, \text{kg}} \]
Calculating:
\[ \Delta v = \frac{10^{-2}}{5 \times 10^{-3}} \]
\[ \Delta v = \frac{10^{-2}}{5 \times 10^{-3}} = \frac{10^{-2}}{5 \times 10^{-3}} = \frac{10^{-2} \times 10^{3}}{5} = \frac{10^{1}}{5} = 2 \, \text{m/s} \]
### Final Answers
- Impulse: \( 10^{-2} \, \text{N s} \)
- Change in velocity: \( 2 \, \text{m/s} \)
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