Given that

Mass of the block m = 15 kg

Coefficient of static friction \mu = 0.18

Acceleration of the trolley a = 0.5 m/s^2

Acceleration due to gravity g = 9.8 m/s^2   

Time taken, t = 20 seconds


Case (a):

Force applied on the block due to its motion F = ma

F = 15 kg * 0.5 m/s^2

F = 7.5 kg m/s^2 = 7.5 N

Static frictional force F_s = \mu N = \mu mg

F_s = 0.18 * 15 kg * 9.8 m/s^2

F_s = 26.46 N

Frictional force is grater than the force applied on the block

The block will remain stationary with respect to the trolley, because the force experienced by the block is less than the static frictional force.

After the 20 seconds the trolly moves with an uniform speed. Thus, the speed change is zero. So It accelerates to zero.( a = 0 )

When acceleration is zero the the block is stationary with respect to the trolley.

Case (b);

Because there is no relative motion between him and the trolley and the block, the block seems to be stationary to an observer going with it.