A vertically projected particle passes the same point at times t₁ and t₂. The magnitude of its velocity while passing that point is:
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A vertically projected particle passes the same point at times t₁ and t₂. The magnitude of its velocity while passing that point is:

G1 Physics · Accepted Answer

The highest point is reached midway in time between the two crossings. Time from the first crossing to the highest point is (t₂−t₁)/2. Since velocity becomes zero there, v = g(t₂−t₁)/2. The two crossing velocities have equal magnitude and opposite directions.