If a ship of mass ` 4 xx 10 ^( 7 ) ` kg initially at rest is pulled by a force of ` 5 xx 10 ^ ( 4 ) ` N through a distance of 4 m, then the speed of the ship will be (resistance due to water is negligible )

Options

A. ` 5 ms ^( - 1 ) `
B. `1.5 ms ^( - 1 ) `
C. `60 ms ^( -1) `
D. `0.1 ms^( - 1 ) `

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Mass of the ship, \( m = 4 \times 10^7 \) kg
- Force applied, \( F = 5 \times 10^4 \) N
- Distance moved, \( s = 4 \) m
- Initial velocity, \( u = 0 \) m/s (the ship is initially at rest)

### Step 2: Calculate the acceleration using Newton's second law
According to Newton's second law of motion, the force is equal to mass times acceleration:
\[ F = m \cdot a \]
Rearranging this gives:
\[ a = \frac{F}{m} \]
Substituting the known values:
\[ a = \frac{5 \times 10^4}{4 \times 10^7} \]
Calculating the acceleration:
\[ a = \frac{5}{4} \times 10^{-3} = 1.25 \times 10^{-3} \text{ m/s}^2 \]

### Step 3: Use the kinematic equation to find the final velocity
We will use the kinematic equation:
\[ v^2 = u^2 + 2as \]
Substituting the known values:
\[ v^2 = 0^2 + 2 \cdot (1.25 \times 10^{-3}) \cdot 4 \]
Calculating:
\[ v^2 = 0 + 2 \cdot 1.25 \times 10^{-3} \cdot 4 = 10 \times 10^{-3} = 0.01 \]
Taking the square root to find \( v \):
\[ v = \sqrt{0.01} = 0.1 \text{ m/s} \]

### Final Answer
The speed of the ship will be \( 0.1 \) m/s.

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