A stone is thrown horizontally . in 0.5 seconds after the stone began to move, the magnitude of it’s velocity is 1.5 times its initial velocity . find the initial velocity

Dear Student,
initial velocity=u
final velocity=v=1.5u
t=0.5s

v=u+at
=>1.5u=u+ax0.5
=>a=u

S=ut+at²/2
=>S=0.625u

We can get one unknown if 2 are known in each equation of motion. But in every equation we have two unknown quantities.
Hence it is not possible to find exact values of initial velocity until acceleration or distance travelled in 0.5s is given.