The velocity acquired by a body moving with uniformaccelertion is `30 m s^(-1)` in `2s` and `60 ms ^(-1)` in `4 s`, The initial velocity is .

Options

A. zero
B. ` 2ms^(-1)`
C. `3 ms^(-1)`
D. `10ms^(-1)`

Explanation

To solve the problem, we need to find the initial velocity of a body moving with uniform acceleration given two conditions of velocity at specific times.

### Step-by-Step Solution:

1. **Identify the given values**:
- At time \( t_1 = 2 \, \text{s} \), the velocity \( v_1 = 30 \, \text{m/s} \).
- At time \( t_2 = 4 \, \text{s} \), the velocity \( v_2 = 60 \, \text{m/s} \).

2. **Calculate the acceleration**:
- We can find the acceleration \( a \) using the formula:
\[ a = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1} \]
- Substituting the values:
\[ a = \frac{60 \, \text{m/s} - 30 \, \text{m/s}}{4 \, \text{s} - 2 \, \text{s}} = \frac{30 \, \text{m/s}}{2 \, \text{s}} = 15 \, \text{m/s}^2 \]

3. **Use the equation of motion to find the initial velocity**:
- The equation of motion we will use is:
\[ v = u + at \]
- Rearranging this to find the initial velocity \( u \):
\[ u = v - at \]
- We can use the first condition (at \( t_1 \)):
\[ u = v_1 - a \cdot t_1 \]
- Substituting the known values:
\[ u = 30 \, \text{m/s} - (15 \, \text{m/s}^2 \cdot 2 \, \text{s}) = 30 \, \text{m/s} - 30 \, \text{m/s} = 0 \, \text{m/s} \]

4. **Conclusion**:
- The initial velocity \( u \) is \( 0 \, \text{m/s} \).

### Final Answer:
The initial velocity is \( 0 \, \text{m/s} \).

---