The correct option is A is four times the velocity at any moment.
We know that, Kinetic energy K=12mv2
Differentiating on both sides with respect to time, we get
dKdt=mv.dvdt
dKdt=(mdvdt)v=(ma)v
From the data given in the question,
m=2 kg and a=2 m/s2
∴dKdt=4v .....(1)
Since the given acceleration is constant, we can use kinematic formulae
Using, v=u+at in (1), we get
dKdt=4u+4at=8(1+t)
So, option (d) is wrong.
From (1), we can conclude that option (c) is also wrong.
Using v2=u2+2as in (1) and substituting the values, we get
dKdt=8√1+2s
So, option (b) is also wrong.
Thus, option (a) is the correct answer.