Please explain is the v0 means automonous velocity , so the velocity of the money would be when the interest rate is zero?

The slope of the LM curve To be able to calculate the interest rate as function of production and money supply, we assume that velocity is a linear function of the interest rate: V = vo+ vi. Here, v, measures how velocity changes with the interest rate. A higher v, means that velocity increases a lot when the interest rate increases. Now the money market equilibrium condition is M (vo + vi) = PY. Dividing by M on both sides and subtracting vo on both sides we get PY Vi= - Vo. M Dividing by v, we get the interest rate: 1 Y i=- Vo V, M/P VI This is the equation for the LM curve. The effect of production on the interest rate is found by differentiating with respect to Y: 1 AY Ai = v, M/P