A stone is thrown vertically upward with an initial velocity v0. Find the distance travelled in time 3vo/2g
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t = 3u/2g
Here, u (or vo, as you wrote) is the initial velocity
g is the acceleratio due to gravity which is -9.8 m/s^2 (as the ball is being thrwon upwards, the acceleration will be negative)
Use the second equation of motion:
s = ut + 1/2×at^2
Plug in the values and solve.
=> s = u(3u/2g) - 1/2(g)(9u^2/4g^2)
=> s = 3u^2/2g - 9u^2/8g
Take the LCM.
=> s = (12u^2 - 9u^2)/8g
=> s = 3u^2/8g
Hope it helps! :)
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