Do you know any examples of this behavior or something similar?

Let's see...

GameObject yourObject = null;
bool hasTouched = false;
Vector2 lastPos = Vector3.zero;

Update()
{
    if(!hasTouched && Input.touchCount == 1) // pressed
    {
        hasTouched = true;
        lastPos = Input.touches[0].position;
        yourObject = Instantiate(someObjectPrefab, lastPos, Quaternion.Identity)
    }
    else if(hasTouched && Input.touchCount == 1) // finger down
    {
        lastPos = Input.touches[0].position;
        yourObject.transform.Position = Camera.main.ViewportToWorldPoint(lastPos);
    }
    else if(hasToched && Input.touchCount == 0) // released
    {
        Vector3 direction = Input.touches[0].position - lastPos;
        yourObject.Rigidbody.velocity = direction.normalized*someSpeedValue;
        hasTouched = false;
    }
}

This is untested and 10-min-hack-something-together code (I haven't Unity installed an that machine here), but it should give you an idea of what you're after