Understanding the problem:

We are given that a freely falling body travels a distance in the last second equal to the distance traveled in the first 3 seconds. We need to find the total time of travel for the body.

Solution:

Let's assume the distance traveled by the body in the first 3 seconds is 'd' units. According to the problem statement, the body travels the same distance 'd' units in the last second.

We know that the distance traveled by a freely falling body in the first second can be calculated using the formula:
d1 = (1/2) * g * t1² [1]

where d1 is the distance traveled in the first second, g is the acceleration due to gravity (approximately 9.8 m/s²), and t1 is the time taken in the first second.

Similarly, the distance traveled by the body in the last second can be calculated using the same formula:
d2 = (1/2) * g * t2² [2]

where d2 is the distance traveled in the last second, and t2 is the time taken in the last second.

Given that d2 = d, we can equate equations [1] and [2]:
(1/2) * g * t1² = (1/2) * g * t2²

Simplifying the equation:
t1² = t2²

Taking the square root of both sides:
t1 = t2

This implies that the time taken in the first second is equal to the time taken in the last second.

Now, let's calculate the total time of travel for the body.

The total distance traveled by the body can be calculated by adding the distances traveled in each second:
Total distance = d1 + d + d2

Substituting the values:
Total distance = (1/2) * g * t1² + d + (1/2) * g * t1²

Simplifying the equation:
Total distance = g * t1² + d

Since t1 = t2, we can write:
Total distance = g * t2² + d

Given that d2 = d, we can rewrite the equation as:
Total distance = g * t2² + d2

Now, let's find the time taken for the body to travel the total distance.

Using the formula for distance traveled in the last second:
Total distance = (1/2) * g * t² + d2

Solving for t:
t² = 2 * (Total distance - d2) / g

Taking the square root of both sides:
t = √[2 * (Total distance - d2) / g]

Therefore, the time taken for the body to travel the total distance is √[2 * (Total distance - d2) / g] seconds.

Conclusion:

In conclusion, if a freely falling body travels a distance in the last second equal to the distance traveled in the first 3 seconds, then the time taken for the body to travel the total distance can be calculated using the formula t = √[2 * (Total distance - d2) / g], where t is the time in seconds, Total distance is the sum of distances traveled in each second, d2 is the distance traveled in the last second, and g is the