A body of mass `2kg` moving on a horizontal surface with an initial velocity of `4 ms^(-1)` 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. 8 N
B. 4 N
C. zero
D. 2 N

Answer

To solve the problem, we need to determine the force required to keep a body of mass 2 kg moving at a constant velocity of 4 m/s on a horizontal surface, given that it comes to rest after 2 seconds due to some opposing force (like friction).

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the body (m) = 2 kg
- Initial velocity (u) = 4 m/s
- Final velocity (v) = 0 m/s (since it comes to rest)
- Time (t) = 2 seconds

2. **Calculate the Acceleration:**
Using the formula for acceleration:
\[ a = \frac{v - u}{t} \]
Substituting the values:
\[ a = \frac{0 - 4}{2} = \frac{-4}{2} = -2 \, \text{m/s}^2 \]
The negative sign indicates that the body is decelerating.

3. **Determine the Force Required to Overcome the Deceleration:**
According to Newton's second law, the force (F) is given by:
\[ F = m \cdot a \]
Since we want to keep the body moving at a constant velocity of 4 m/s, we need to apply a force equal in magnitude but opposite in direction to the deceleration force. Therefore:
\[ F = m \cdot (-a) = 2 \cdot (-(-2)) = 2 \cdot 2 = 4 \, \text{N} \]

4. **Conclusion:**
The force required to keep the body moving at a constant velocity of 4 m/s is **4 N**.

### Final Answer:
The force required is **4 N**.

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