The given problem involves the motion of a stone dropped from the top of a tower. We are given that the stone travels a distance of 25m in the last second of its motion. We are also given that the acceleration due to gravity, g, is 10m/s^2. We need to determine the total time of fall.

To solve this problem, we can use the equations of motion for uniformly accelerated motion. These equations relate the displacement, time, initial velocity, final velocity, and acceleration of an object.

Let's break down the problem into smaller steps to find the solution:

Step 1: Determine the acceleration of the stone
Given that the acceleration due to gravity, g, is 10m/s^2, we can assume that the stone is only under the influence of gravity and there is no other external force acting on it. Therefore, the acceleration of the stone is equal to the acceleration due to gravity, g.

Step 2: Determine the time taken for the stone to travel 25m in the last second
We are given that the stone travels a distance of 25m in the last second of its motion. This means that the stone covered this distance in the final second before hitting the ground. Let's assume that the total time of fall is T seconds. Therefore, the time taken to travel the last 25m is T - 1 seconds (as the last second is excluded).

Using the equation of motion for displacement, we have:
s = ut + (1/2)at^2

Since the initial velocity, u, is 0 (as the stone is dropped), the equation simplifies to:
s = (1/2)at^2

Plugging in the values, we have:
25 = (1/2)(10)(T - 1)^2

Simplifying the equation, we get:
25 = 5(T - 1)^2

Step 3: Solve the equation for T
Expanding and rearranging the equation, we have:
(T - 1)^2 = 5

Taking the square root of both sides, we get:
T - 1 = sqrt(5)

Adding 1 to both sides, we have:
T = sqrt(5) + 1

Step 4: Determine the total time of fall
Since the total time of fall, T, is equal to the time taken to travel the last 25m plus 1 second, we have:
Total time of fall = T + 1 = sqrt(5) + 1 + 1 = sqrt(5) + 2

Therefore, the total time of fall is approximately sqrt(5) + 2 seconds.

To summarize:
- The stone travels a distance of 25m in the last second of its motion.
- Using the equation of motion for displacement, we determine that the total time of fall is equal to sqrt(5) + 2 seconds.

25=0+1/2×10(2t-1) =t=3s