A body of mass 1 kg moving on a horizontal surface with an initial velocity of 6m/s comes to rest after 3 seconds. If one wants to keep the body moving on the same surface with the same velocity of 6m/s, then the force required is

Options

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

Answer

To solve the problem step by step, we will analyze the motion of the body and determine the force required to keep it moving at a constant velocity of 6 m/s.

### Step 1: Identify the given data
- Mass of the body (m) = 1 kg
- Initial velocity (u) = 6 m/s
- Final velocity (v) = 0 m/s (after 3 seconds)
- Time (t) = 3 seconds

### Step 2: Calculate the acceleration
Using the first equation of motion:
\[ v = u + at \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

Rearranging the equation to find acceleration \( a \):
\[ a = \frac{v - u}{t} \]

Substituting the known values:
\[ a = \frac{0 - 6}{3} = \frac{-6}{3} = -2 \, \text{m/s}^2 \]

This negative sign indicates that the acceleration is acting in the opposite direction to the motion, which is consistent with the body coming to rest.

### Step 3: Determine the force required to keep the body moving
To keep the body moving at a constant velocity of 6 m/s, we need to counteract the deceleration (or negative acceleration) that is acting on the body. The force required can be calculated using Newton's second law:
\[ F = ma \]

Since we want to maintain the velocity, we need to apply a force equal in magnitude but opposite in direction to the deceleration:
\[ F = m \times |a| \]

Substituting the values:
\[ F = 1 \, \text{kg} \times 2 \, \text{m/s}^2 = 2 \, \text{N} \]

### Conclusion
The force required to keep the body moving at a constant velocity of 6 m/s is **2 N**.

---