A force of 5 N acts on a 15 kg body initially at rest. The work done by the force during the first second of motion of the body is

Options

A. 5J
B. `(5)/(6)J`
C. `6J`
D. `75J`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Force (F) = 5 N
- Mass (m) = 15 kg
- Initial velocity (u) = 0 m/s (since the body is initially at rest)
- Time (t) = 1 s

### Step 2: Calculate the acceleration
Using Newton's second law of motion, we can find the acceleration (a) using the formula:
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{5 \, \text{N}}{15 \, \text{kg}} = \frac{1}{3} \, \text{m/s}^2 \]

### Step 3: Calculate the displacement during the first second
Since the body starts from rest, we can use the formula for displacement (s) under uniform acceleration:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ s = 0 \cdot 1 + \frac{1}{2} \cdot \frac{1}{3} \cdot (1)^2 \]
\[ s = 0 + \frac{1}{2} \cdot \frac{1}{3} \cdot 1 = \frac{1}{6} \, \text{m} \]

### Step 4: Calculate the work done
The work done (W) by the force is given by the formula:
\[ W = F \cdot s \]
Substituting the values we have:
\[ W = 5 \, \text{N} \cdot \frac{1}{6} \, \text{m} \]
\[ W = \frac{5}{6} \, \text{J} \]

### Final Answer
The work done by the force during the first second of motion of the body is \(\frac{5}{6} \, \text{J}\).

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