First of all make sure you have Touch added (do so in layout view).
Then do something like:
On Object Tap
Apply Impulse in opposite direction
If you are using Physics it will take some playing with to get it how you want. You mentioned impulse but if you want a gradual acceleration/deceleration you should use force. Impulse is like a ball hitting a bat or an explosion; Force is like a car/bicycle/jetpack accelerating.
If I am picturing correctly in my head how you might want it to look try this:
Add a instance variable to the object (numerical). I will refer to this variable as state but call it what you want.
For our reference:
On touch if state = 0 then change state to 1
If state = 1
If velocity < (desired velocity here) then apply force
If velocity >= (desired velocity) then state = 2
If state = 2
Trigger only once -> Wait desired float time then state = 3
If state = 3
If velocity > 0 Then apply force in opposite direction or some other method to slow the object
If velocity = 0 (or less than 0 if gravity taking hold) Then state = 0 (thus being ready for the touch even again)
That's just off the top of my head so there might be a flaw in there but give it a try and let me know how it works