A force 100 N acts on a body of mass 2 kg for 10 s. The change in velocity of the body is

Options

A. `100 m s^(-1)`
B. ` 250 m s^(-1)`
C. ` 500 m s^(-1)`
D. `1000 m s^(-1)`

Explanation

To find the change in velocity of a body when a force acts on it, we can use the impulse-momentum theorem. Here’s the step-by-step solution:

### Step 1: Understand the given data
- Force (F) = 100 N
- Mass (m) = 2 kg
- Time (Δt) = 10 s

### Step 2: Write the impulse-momentum theorem
The impulse-momentum theorem states that the impulse (force multiplied by time) is equal to the change in momentum of the object. Mathematically, it can be expressed as:
\[ I = F \cdot \Delta t = \Delta p \]
where \( \Delta p \) is the change in momentum.

### Step 3: Express change in momentum
Change in momentum can also be expressed in terms of mass and velocity:
\[ \Delta p = m \cdot v - m \cdot u \]
where \( v \) is the final velocity and \( u \) is the initial velocity.

### Step 4: Relate impulse to change in velocity
From the impulse-momentum theorem, we can equate the two expressions:
\[ F \cdot \Delta t = m \cdot v - m \cdot u \]
This can be rearranged to find the change in velocity:
\[ v - u = \frac{F \cdot \Delta t}{m} \]

### Step 5: Substitute the known values
Now, substitute the values into the equation:
\[ v - u = \frac{100 \, \text{N} \cdot 10 \, \text{s}}{2 \, \text{kg}} \]

### Step 6: Calculate the change in velocity
Calculating the right side:
\[ v - u = \frac{1000 \, \text{Ns}}{2 \, \text{kg}} \]
\[ v - u = 500 \, \text{m/s} \]

### Final Answer
The change in velocity of the body is **500 m/s**.

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