Problem Statement:
A body starting from rest has an acceleration of 4m/s². Calculate the distance traveled by it in the 5th second.

Solution:

To solve this problem, we can use the equations of motion. The equation that relates distance, initial velocity, acceleration, and time is:

Distance (s) = Initial Velocity (u) * Time (t) + (1/2) * Acceleration (a) * Time (t)²

In this case, the body starts from rest, so the initial velocity (u) is 0 m/s. The acceleration (a) is given as 4 m/s², and we need to find the distance traveled in the 5th second, which means the time (t) is 5 seconds.

Let's substitute the given values into the equation:

Distance (s) = 0 * 5 + (1/2) * 4 * 5²
Distance (s) = 0 + (1/2) * 4 * 25
Distance (s) = 0 + 2 * 25
Distance (s) = 0 + 50
Distance (s) = 50 meters

Therefore, the distance traveled by the body in the 5th second is 50 meters.

Explanation:

The equation of motion used to solve this problem is derived from the basic principles of kinematics. It relates the distance traveled by an object to its initial velocity, acceleration, and time. In this case, since the body starts from rest, the initial velocity is 0 m/s.

The equation consists of two terms. The first term represents the distance covered due to the initial velocity, which is 0 in this case. Thus, the first term becomes 0.

The second term represents the distance covered due to the acceleration. Since the acceleration is constant, we can use the equation (1/2) * a * t² to calculate this distance. Plugging in the values of acceleration (4 m/s²) and time (5 seconds), we find that the distance covered due to acceleration is 50 meters.

Adding the two terms, we find that the total distance traveled by the body in the 5th second is 50 meters.

Key Points:
- The distance traveled by an object can be calculated using the equation: s = ut + (1/2)at²
- When the object starts from rest, the initial velocity (u) is 0 m/s.
- The acceleration (a) is given as 4 m/s².
- We need to find the distance traveled in the 5th second, so the time (t) is 5 seconds.
- Substituting the values into the equation, we find that the distance traveled is 50 meters.