A body of mass `2kg` moving on a horizantal surface with an initial velocity of comes to rest after `2` second. If one wants to keep this body moving on the same surface with a velocity of `4 ms^(-1)` the force required is

Options

A. zero
B. `2 N`
C. `4 N`
D. `8 N`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the Given Information
- Mass of the body, \( m = 2 \, \text{kg} \)
- Initial velocity, \( u = 4 \, \text{m/s} \)
- Final velocity after 2 seconds, \( v = 0 \, \text{m/s} \)
- Time taken to come to rest, \( t = 2 \, \text{s} \)

### Step 2: Calculate the Deceleration
Using the formula for acceleration:
\[ v = u + at \]
Substituting the known values:
\[ 0 = 4 + a \cdot 2 \]
Rearranging gives:
\[ a \cdot 2 = -4 \implies a = -2 \, \text{m/s}^2 \]
This indicates that the body is decelerating at \( 2 \, \text{m/s}^2 \).

### Step 3: Determine the Required Force to Maintain Constant Velocity
To keep the body moving at a constant velocity of \( 4 \, \text{m/s} \), we need to counteract the deceleration. The effective acceleration required to maintain constant velocity is \( 0 \, \text{m/s}^2 \).

Let \( A_1 \) be the acceleration due to the applied force. The net effective acceleration \( A_{\text{effective}} \) can be expressed as:
\[ A_{\text{effective}} = A_1 + a \]
Setting \( A_{\text{effective}} = 0 \) (for constant velocity):
\[ 0 = A_1 - 2 \]
Thus,
\[ A_1 = 2 \, \text{m/s}^2 \]

### Step 4: Calculate the Force Required
Using Newton's second law:
\[ F = m \cdot A_1 \]
Substituting the values:
\[ F = 2 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 4 \, \text{N} \]

### Final Answer
The force required to keep the body moving at a constant velocity of \( 4 \, \text{m/s} \) is \( 4 \, \text{N} \).

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