1. a farmer moves along the boundary of his rectangular field of side 10m x 20m . farmer covers 1m in 1sec . what will be the magnitude of displacement at the total distance travelled.
2 . rahul pedals his cycle from rest. pedals his cycle to get a
velocity of 10 ms-1 in 30 seconds.
then he applies brakes in such that the velocity of the cycle comes does to 6
ms-1 in next 5 seconds . calculate
the acceleration and deceleration .

1). He's walking the 'perimeter' of his field, meaning 'the distance all the way around'.
If he stays right along the fence all the way, then the total distance he walks is
(10 + 20 + 10 + 20) = 60 meters. (It's a small field ... about 5% of an acre.)
The magnitude of displacement is the distance between the start point and end point,
regardless of the route.  After he finishes one whole trip around, his displacement is
zero, because he ends up at the same place where he started.
Notice the big fat red herring in the question: None of this depends on the speed
at which he walks.

2).  Acceleration = (change in speed) / (time for the change)

While speeding up, acceleration = (10 - 0) / 30 = 1/3 meter per second².

While slowing down, deceleration = (6 - 10) / 5 = -4/5 = -0.8 meter per second²

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.