Mr Money Mustache recently posted a writeup for a conversion for about $1000. I think you could do the same conversion for less if you source your kit and battery cheaper- these same kits sell for less on ebay.
Just get some smooth tread tires that will be better for pavement travel.
2.2 miles takes about 40 minutes to walk.
On a bike and mostly flat terrain, 10-15 minutes max.
Unless the commute is a steeply graded 2.2 mile slope the motor seems overkill and providing little if any benefit to travel time or enjoyment. Wouldn't you rather get to work with a little endorphin rush?
Maybe ride the route first after work or on a weekend to show yourself you can do it. But after a commute or two you will quickly see it's nothing and likely want to ride even further.
Indeed knobbly tyres and MTB-style frames are one of the worst things to have happened to non-leisure cycling in the UK.
People buy a cheap MTB from Halfords, use it casually a few times out with the kids and then try commuting on it perhaps as part of a Cycling Week. After a couple of attempts it goes back into the garage.
Outside Oxford and Cambridge, traditional road-going non-racing frames are quite rare.
So-called hybrid bikes seem like the most commonly sold bike in north america. Flat bars, 700c wheels, mid-thin tires (32-40 mm), geometry either can be somewhat sporty or more laid back.
Just wish more would come with accesories useful to most utilitarian cyclists. Fenders, lights, racks/baskets, and chain guard. Man, chain guards are so hard to come upon in NA, I really envy european bikes for that. I suspect for most peopl it's #1 reason for not cycling in regular/work/office clothes
In the US, folks buy older, non-suspension mountain bikes, and convert them to commuting use by adding street tires and whatever other accessories they desire (rack, fenders, etc.). The result is a fairly comfortable, utilitarian bike, that's not a theft magnet.
The biggest expense is usually the battery -- the one I got (700 watt hours) was about 500 (with shipping), and it can get me from 30 - 60 miles (hard throttle only vs. taking it easy and pedal assist). Lunacycle is now selling a small size pack that is about 1/2 the capacity of min (about 300 watt hours) for $230, plus $30 shipping, and you will need a charger (another $35 - $70).
A decent hub motor kit starts off at around $350 from a reputable vendor, you can either put on a front or rear hub motor. I've heard good things about the Golden Motor's magic pie kit (and variations) -- this is a direct drive from $325 to $375 or so, but since it is direct drive I would put it on the back wheel myself. The only front wheel conversion I would do would be a geared motor.
http://www.mrmoneymustache.com/2016/05/25/recipe-for-a-badas...