A body starts from rest and moves along a straight line path with uniform acceleration. The ratio of velocities at t = 1s and t = 2 s is ______.

Options

A. `2:1`
B. `1:2`
C. `1:sqrt(2)`
D. `sqrt(2):1`

Answer

To solve the problem, we need to find the ratio of velocities of a body moving with uniform acceleration at two different times: \( t = 1 \) second and \( t = 2 \) seconds.

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- The body starts from rest, which means the initial velocity \( U = 0 \).
- The body moves with uniform acceleration \( A \).

2. **Use the First Equation of Motion**:
- The first equation of motion states that:
\[ V = U + A \cdot t \]
- Since \( U = 0 \), this simplifies to:
\[ V = A \cdot t \]

3. **Calculate Velocity at \( t = 1 \) second**:
- For \( t = 1 \) second:
\[ V_1 = A \cdot 1 = A \]

4. **Calculate Velocity at \( t = 2 \) seconds**:
- For \( t = 2 \) seconds:
\[ V_2 = A \cdot 2 = 2A \]

5. **Find the Ratio of Velocities**:
- Now, we need to find the ratio \( \frac{V_1}{V_2} \):
\[ \frac{V_1}{V_2} = \frac{A}{2A} = \frac{1}{2} \]

6. **Final Answer**:
- The ratio of velocities at \( t = 1 \) second and \( t = 2 \) seconds is:
\[ \frac{1}{2} \]