Question

A body is initially at rest it undergoes one dimensional motion with a constant acceleration how does its displacement (s) depends on time (t)

Answer 1

If the acceleration is constant then the time will be uniform and will be constant for the displacement...
Also if u r senior student u can study the following formula:-.
F=mgh.. and W=F*S..

hope helps u

Answer 2

This could be explained using the 2nd equation of motion.

so you have a body with say initial velocity u and final velocity v , it undergoes uniform accleration a
so, average velocity here could be written as (v+u)/2

so the distance travelled here would be velocity × time

s = (v+u)(t) / 2
as u =0
therefore the equation becomes
s= vt /2 -----(i)


now, use the first equation of motion
i.e (v-u)/t =a
as u =0 therefore,
v = at

we'll do this step in order to replace final velocity, because it isn't mention in the question asked.
so now, substitute for v in eq. (i) and you'll get

(at)(t)/2
s = at^2 /2.

Hence, this given equantion shows the relation between those 2 quantities mentioned above.