Step 1: Understanding the Concept:
When an object moves with a constant (uniform) acceleration in a straight line, its motion can be described by Newton's equations of motion.
In this case, we know the initial velocity, the acceleration, and the time, and we need to find the total distance traveled.
Step 2: Key Formula or Approach:
The second equation of motion relates displacement (\(s\)), initial velocity (\(u\)), time (\(t\)), and acceleration (\(a\)):
\[ s = ut + \frac{1}{2}at^{2} \]
Step 3: Detailed Explanation:
1. List the known variables from the problem:
- Initial velocity (\(u\)) = 0 m/s (as the body starts from rest).
- Acceleration (\(a\)) = 2 m/s\(^2\).
- Time interval (\(t\)) = 5 s.
2. Plug the values into the formula:
\[ s = (0 \times 5) + \frac{1}{2} \times 2 \times (5)^{2} \]
3. Simplify the expression:
The term \( ut \) becomes zero.
The factor \( \frac{1}{2} \times 2 \) cancels out to 1.
\[ s = 0 + 1 \times 25 = 25 \text{ m} \]
4. Verification:
Final velocity \( v = u + at = 0 + 2(5) = 10 \text{ m/s} \).
Distance using average speed: \( \text{Distance} = \left( \frac{0 + 10}{2} \right) \times 5 = 5 \times 5 = 25 \text{ m} \).
Step 4: Final Answer:
The total distance covered by the body in 5 seconds is 25 m.
This matches Option (C).