How would an increase in velocity affect an object that orbits the sun?

At any particular orbital radius, there is only one velocity which will give stable orbit. An increase in velocity would increase the centripetal force, overcoming the gravitational pull, the net force then accelerating the object away from the sun.

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Stable orbit:

(Gravity (G*m1*m2)/d2) = ( centripetal force (m2*(v2/d)) )

G = newtons gravitational constant

m1 = mass sun (kg)

m2 = mass object (kg)

d = distance between sun and object (metres)

v = orbital velocity (metres per second)