N=m(g+g/2)=3mg/2.
u=o,at a=g/2
s=ut+ 1/2at^2
s=1/2g/2t^2
s=gt^2/4

W=NS=3mg/2.gt^2/4
=3mg^2t^2/8

Problem:
A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward. What is the work done by the normal reaction on the block in time t?

Solution:
To find the work done by the normal reaction on the block, we need to understand the concept of work and how it is related to force and displacement.

Work:
Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work is given by the equation:

W = F * d * cosθ

where W is the work done, F is the applied force, d is the displacement, and θ is the angle between the force and displacement vectors.

Normal Reaction:
In this case, the normal reaction is the force exerted by the platform on the block in the upward direction. It counteracts the force of gravity acting on the block and prevents it from sinking into the platform. The normal reaction force is perpendicular to the displacement of the block.

Constant Acceleration:
The platform is accelerating upward with a constant acceleration of g/2. This means that the velocity of the platform is increasing with time, and consequently, the velocity of the block is also increasing.

Analysis:
To find the work done by the normal reaction on the block in time t, we need to determine the displacement of the block during this time period.

Since the platform starts from rest, its initial velocity is zero. The equation of motion for the platform can be given as:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

In this case, the initial velocity of the platform (u) is 0, the acceleration (a) is g/2, and the time (t) is given.

By substituting the values into the equation, we can find the final velocity (v) of the platform.

Similarly, we can find the final velocity of the block by considering that it starts from rest as well.

Once we have the final velocity of the block, we can use the equation:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

We can rearrange this equation to solve for the displacement (s) of the block.

Work Done:
Now that we have the displacement of the block, we can calculate the work done by the normal reaction on the block using the equation:

W = F * d * cosθ

In this case, the force (F) is the normal reaction force, the displacement (d) is the displacement of the block, and θ is the angle between the force and displacement vectors.

Since the normal reaction force is perpendicular to the displacement of the block, the angle θ is 90 degrees and the cosine of 90 degrees is 0.

Therefore, the work done by the normal reaction on the block is zero.

Conclusion:
The work done by the normal reaction on the block in time t is zero. This is because the normal reaction force is perpendicular to the displacement of the block, and the cosine of 90 degrees is 0.