Distance travelled in n time when a body is thrown upwards

1. The problem statement, all variables and given/known data
Here is a question in my text book. I saw the answer, but no explanation was there.

A stone is thrown vertically upward with an initial velocity [itex]v_0[/itex]. The distance travelled by it in time [itex]\frac{1.5v_0}{g}[/itex] is ______________.
Answer is [itex]\frac{5v_0^2}{8g}[/itex].

2. Relevant equations
Max. height reached by a body thrown upwards with an initial velocity v is [itex]\frac{v^2}{2g}[/itex]
Time taken to reach the max.height with initial velocity v=[itex]\frac{v}{g}[/itex]

3. The attempt at a solution

Time taken to travel AB+BC=[itex]\frac{1.5v_0}{g}[/itex]

We know that time taken to travel AB=[itex]\frac{v_0}{g}[/itex]

∴Time taken to travel BC=[itex]\frac{1.5v_0}{g} – \frac{v_0}{g}[/itex]

Initial velocity at B in BC=u=0


We know [itex]v=u+at[/itex]






Distance of AB+BC=[itex]\frac{v_0^2}{2g}+\frac{v_0^2}{8g}[/itex]



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