a stone is thrown vertically upward with an initial velocity v0. the distance travelled by it in time 1.5v0/g?

Answer 1

recall that the motion of the stone is uniformly accelerated motion (because it accelerated due to gravity). thus we can use the formula:
h = vo*t - 1/2(g)(t^2)
where
h = height
vo = initial velocity
t = time
g = acceleration due to gravity = 9.8 m/s^2
substituting,
h = vo*(1.5*vo/g) - (1/2)(g)(1.5*vo/g)^2
h = 1.5*[(vo)^2]/g - 1.125*[(vo)^2]/g
h = 0.375*[(vo)^2]/g

hope this helps~ :)