Given:
- The body starts falling from a height 'h'.
- The body travels a distance of h/2 during the last second of motion.

To find:
- The time of travel in seconds.

Assumptions:
- We are assuming the body falls freely under the influence of gravity.
- The body is not affected by air resistance.

Calculating the time of travel:
Let's consider the motion of the body in two parts: the first part before the last second, and the second part during the last second.

First part:
- In the first part, the body falls from height h - h/2 = h/2.
- The time taken to fall this distance can be calculated using the equation for free fall motion:
h = (1/2) * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time.
- Substituting the given values, we have:
h/2 = (1/2) * g * t^2.
- Dividing both sides of the equation by (1/2)g, we get:
t^2 = (h/2) / ((1/2)g).
- Simplifying further, we have:
t^2 = h / g.
- Taking the square root of both sides, we get:
t = sqrt(h / g).

Second part:
- In the last second of motion, the body travels a distance of h/2.
- The time taken to travel this distance is 1 second.

Total time of travel:
The total time of travel is the sum of the time taken in the first part and the time taken in the second part.
- t_total = t + 1.
- Substituting the value of t from the first part, we have:
t_total = sqrt(h / g) + 1.

Final answer:
The time of travel is given by t_total = sqrt(h / g) + 1.
- Since the answer is in seconds, it is not necessary to simplify the expression further.

Therefore, the time of travel is 2√2 seconds.