A block of mass m is kept on a platform which starts from rest with a constant acceleration g/2 upwards, as shown in the figure. Work done by normal reaction on block in time t is___?

Since the acceleration is in the upward direction, there will be a pseudo force acting on the block given as: Fp = m × g/2
Now applying the force balance on the block
N - mg = mg/2 ⇒ N = 3mg/2
We know that the displacement of a body moving under constant acceleration is given as
S = ut + (1/2)at²
Here initial velocity u is zero and acceleration a = g/2.
Therefore, displacement S = (1/2)(g/2)t² = gt²/4
Now, work done W = ∫F⋅ds = N⋅S (since N is constant)
W = (3mg/2)(gt²/4) ⇒ W = 3mg²t²/8