A body of mass 2 kg is moving with a velocity `8m//s` on a smooth surface. If it is to be brought to rest in 4 seconds, then the force to be applied is

Options

A. 8 N
B. 4 N
C. 2 N
D. 1 N

Answer

To solve the problem step by step, we need to find the force required to bring a body of mass 2 kg, moving at a velocity of 8 m/s, to rest in 4 seconds.

### Step 1: Identify the given values
- Mass of the body (m) = 2 kg
- Initial velocity (u) = 8 m/s
- Final velocity (v) = 0 m/s (since the body is brought to rest)
- Time (t) = 4 seconds

### Step 2: Use the first equation of motion to find acceleration
The first equation of motion states:
\[ v = u + at \]
Where:
- \( v \) is the final velocity
- \( u \) is the initial velocity
- \( a \) is the acceleration
- \( t \) is the time

Substituting the known values into the equation:
\[ 0 = 8 + a \cdot 4 \]

### Step 3: Rearrange the equation to solve for acceleration (a)
Rearranging the equation gives:
\[ a \cdot 4 = -8 \]
\[ a = \frac{-8}{4} \]
\[ a = -2 \, \text{m/s}^2 \]

### Step 4: Calculate the force using Newton's second law
Newton's second law states:
\[ F = m \cdot a \]
Where:
- \( F \) is the force
- \( m \) is the mass
- \( a \) is the acceleration

Substituting the values of mass and acceleration:
\[ F = 2 \cdot (-2) \]
\[ F = -4 \, \text{N} \]

### Step 5: Interpret the result
The negative sign indicates that the force is applied in the opposite direction of the motion (which is expected since we are trying to bring the body to rest). Therefore, the magnitude of the force required is:
\[ F = 4 \, \text{N} \]

### Final Answer
The force to be applied is **4 N** in the direction opposite to the motion.

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