A force of 6 N acts on a body at rest and mass 1 kg. During this time, the body attains a velocity of 30 m/s. The time for which the force acts on the body is

Options

A. 10 sec
B. 8 sec
C. 7 sec
D. 5 sec

Explanation

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

### Step 1: Identify the given values
- Force (F) = 6 N
- Mass (m) = 1 kg
- Final velocity (v) = 30 m/s
- Initial velocity (u) = 0 m/s (since the body is at rest)

### Step 2: Calculate the acceleration
Using Newton's second law of motion, we can find the acceleration (a) using the formula:
\[ F = m \cdot a \]

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

Substituting the known values:
\[ a = \frac{6 \, \text{N}}{1 \, \text{kg}} = 6 \, \text{m/s}^2 \]

### Step 3: Use the kinematic equation to find time
We can use the first equation of motion:
\[ v = u + a \cdot t \]

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

Substituting the known values:
\[ t = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{6 \, \text{m/s}^2} \]
\[ t = \frac{30 \, \text{m/s}}{6 \, \text{m/s}^2} = 5 \, \text{s} \]

### Final Answer
The time for which the force acts on the body is **5 seconds**.

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