Question

The distance x covered in time t by a body having initial velocity

Answer 1

Explanation:

The equations that you have quoted are called kinematic equations.

The dictionary definition of kinematics is:

the branch of mechanics that deals with pure motion, without reference to the masses or forces involved in it

So kinematic equations are not derived from Newton's laws of motion.

They would be correct irrespective of whether or not Newton's laws of motion were correct.

However dynamics

the branch of mechanics concerned with the motion of bodies under the action of forces

is very much to do with Newton's laws of motion.