Forget the freeway.

For a real appreciation of Tesla’s all-electric Model 3 sedan, try a winding drive up the old Mount Hamilton Road, a thousand feet above San Jose.

Granted, you won’t be going very fast, considering the entire road is one Hummer wide. But the paperclip curves with their knee-high guardrails feel a lot less terrifying in a car whose low center of gravity glues it to the road. (Thank you, big floorboard battery pack.)

When the coast is clear, you can dart past struggling cyclists faster than a spooked deer, then return immediately to a more sensible speed without touching the brakes. And eventually, you realize just how little you’re thinking about the act of driving itself, with no shifting, no grinding gears and almost no noise beyond the wind to distract you.

The $35,000 Model 3 is the culmination of Tesla CEO’s Elon Musk’s long-term strategy, a mass-market electric car that looks and feels much like the high-priced luxury sedans Tesla has sold since 2012. Its launch has not gone smoothly.

After Musk handed over the first few Model 3 sedans to Tesla employees in July, production stubbornly failed to take off, even as more than 450,000 reservation holders waited for their cars. Deliveries to the public at large began in late December, and only in the past month has the Model 3 become a common sight on Bay Area roads.

Now Playing:

So is it worth the wait?

To get a sense, Chronicle photographer Lea Suzuki and I spent an afternoon with the Model 3, cruising Silicon Valley’s freeways, city streets, and yes, that crazy Mount Hamilton Road.

The version I drove — the only one currently in production — comes with the Model 3 “premium upgrade package” and costs $57,500. Tesla did the same thing with the Model S and the Model X sport utility vehicle, launching production with more expensive editions before making the basic versions. The company plans to begin building the $35,000 Model 3 this year.

While it’s impossible to know how the less-expensive Model 3 will compare, the souped-up version impresses.

From the outside, the Model 3 can be hard to distinguish from its bigger sibling — the Model S — except for a few telltale signs. The manual door handles curve up at the end, the T-shaped Tesla badge sits squarely on the hood, and there’s nothing on the front even approximating a grille.

The inside, however, is the real departure.

There is no dashboard of any kind other than a single, 15-inch touch-screen to the right of the wheel. No speedometer, no odometer and, of course, no gas gauge. Air vents have been replaced by a horizontal slit that stretches the entire way across the front of the cabin. That opening has no visible moving parts, but you can aim the air stream quite precisely by using the touch-screen.

Although the Model 3 is 1 foot shorter than the S, the cabin does not feel cramped, either in the front or back. The ceiling helps. In the version of the car I drove, tinted roof windows stretch over both the front and back seats.

Punching the accelerator won’t fling you back in the driver’s seat quite the way it will in the Model S or Model X, but the car can still jump from zero to 60 mph in 5.1 seconds (5.6 seconds for the $35,000 version). And like most modern EVs, acceleration feels instantaneous. On an uncrowded freeway, the smooth and quiet electric motor makes it extremely easy to lose track of your speed. Glance occasionally at the touch-screen, which posts speed in the upper left corner, and you may be surprised.

Engage the Autopilot system (which costs $5,000), and the car will keep its lane and speed, adjusting as needed if other cars pop in front of you. Take your hands off the wheel for more than a few seconds, however, and the screen will start pulsing blue to get your attention. Ignore it, and the car will scold you with pings.

The Model 3 is a far more interesting car, however, on a twisting road.

All Teslas feature regenerative braking, a system that captures some of the kinetic energy of a moving car and uses it to recharge the battery. Take your foot off the accelerator, and the car immediately starts slowing down, even before you touch the brake pedal. It feels like having two separate braking systems working at once, and for drivers who haven’t experienced it before, it takes some adjustment.

But getting used to it pays off. On a winding road, almost all the driving gets done with one pedal. As fast as the Model 3 can be, the ability to both speed up and slow down by working the accelerator gives a greater sense of control than a typical car allows. By the time we passed the GrandView Restaurant, heading toward the Lick Observatory, it felt perfectly natural.

The effect is even better going downhill. On the long descent to the valley floor, I did not touch the brake pedal until we reached a stop sign just outside San Jose city limits. And yet, I always felt I was going exactly the speed I wanted, even when it was just 15 miles per hour. With no need to rein in an automatic transmission trying to accelerate downhill, I could focus solely on the road, the green hills and the jaw-dropping view.

And that, perhaps, is one of the car’s best features. Driving it doesn’t feel like work.

David R. Baker is a San Francisco Chronicle staff writer. Email: dbaker@sfchronicle.com Twitter: @DavidBakerSF