A force of 16 N acts on a body at rest having mass 2 kg. During this time, the body attains a velocity of 32 m/s. The time for which the force acts on the body is

Options

A. 10 sec.
B. 8 sec.
C. 7 sec.
D. 4 sec.

Answer

To solve the problem step by step, we will use Newton's second law of motion and the equations of motion.

### Step 1: Identify the given values
- Force (F) = 16 N
- Mass (m) = 2 kg
- Final velocity (v) = 32 m/s
- Initial velocity (u) = 0 m/s (since the body is at rest)

### Step 2: Use Newton's second law to find acceleration
According to Newton's second law:
\[ F = m \cdot a \]
Where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.

Rearranging the formula to find acceleration:
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{16 \, \text{N}}{2 \, \text{kg}} = 8 \, \text{m/s}^2 \]

### Step 3: Use the equation of motion to find time
We can use the first equation of motion:
\[ v = u + a \cdot t \]
Where:
- \( v \) is the final velocity,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.

Rearranging the equation to solve for time \( t \):
\[ t = \frac{v - u}{a} \]

Substituting the known values:
\[ t = \frac{32 \, \text{m/s} - 0 \, \text{m/s}}{8 \, \text{m/s}^2} \]
\[ t = \frac{32}{8} = 4 \, \text{s} \]

### Final Answer
The time for which the force acts on the body is **4 seconds**.

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