Understanding the Situation:
The particle starts from rest, meaning its initial velocity is 0, and it has a uniform acceleration a. After n seconds, its velocity becomes v.

Calculating Displacement in the Last Two Seconds:
To find the displacement of the body in the last two seconds, we need to break down the problem step by step.
1. Calculate the Final Velocity:
Using the equation of motion, we know that the final velocity (v) after n seconds can be calculated as:
v = u + at, where u is the initial velocity (0) and t is the time in seconds.
2. Calculate the Acceleration:
Since the particle has a uniform acceleration a, the acceleration remains constant. Therefore, we can use the equation of motion to find the acceleration:
v = u + at
=> a = (v - u) / t
3. Find the Displacement in the Last Two Seconds:
To find the displacement in the last two seconds, we need to calculate the velocity at (n-2) seconds. Using the same equation of motion:
v' = u + a(n-2)
4. Calculate the Displacement:
Now, to find the displacement in the last two seconds, we can use the equation of motion:
s = ut + (1/2)at^2
=> s = 0 + (1/2)av^2

Explanation of Displacement Calculation:
The displacement of the body in the last two seconds is calculated by finding the final velocity at (n-2) seconds and then using the equation of motion to determine the displacement based on this velocity and the acceleration. This approach breaks down the problem into manageable steps and allows for a systematic calculation of the displacement.