physics behind why accelerating then decelerating takes more fuel than constant speed?

Interesting question.

You do have a good point. Only effects which dissipate energy as heat actually cause net fuel consumption (for flat roadways).

What effects do cause heat dissipation?

The inertia of the car and machinery?...NO, wrong. Inertia causes storage of work as kinetic energy, and when the car slows down you get that work back in theory. ALL the previous posters have screwed up on this one.

Axle friction? Yes. Except...this is a dry friction, and energy dissipated by dry friction is independent of speed.

Air drag? Yes. This is the velocity dependent factor. And even some axle friction due to lubricated parts.

There is another factor which isn't obvious to us...how the engine itself works. Engines prefer to operate at a constant rotational speed. If you do pulse-coast driving, during the "pulse" periods, the car will extract MUCH more fuel than it would need otherwise.

The efficiency of a real car's engine (not an ideal car's engine) does depend on the desired power output. This is what causes the problem with pulse-coast driving. Demanding the maximum power out of your engine is far less efficient than just demanding a steady power output at a value less than upper limit of power output.

Acceleration is a vector, defined as the derivative of velocity (not speed) with respect to time. Since velocity is a vector with a speed and direction, even if the speed is constant if the direction is changing there is an acceleration occurring. A physical example of this is centripetal force. Drive a car at a constant speed in a circle. You'll feel the force pushing you outwards radially. Since you're feeling a force acting and F=mA you know there's an acceleration occurring even if the speedometer stays fixed.

Accelerating takes more applied force than running at a constant speed does. The more rapid the acceleration, the more force must be applied. More force means more enery input, = more fuel.

If you were moving at a constant speed, deceleration would only be required if you are stopping. This could be by just backing off the gas, and coasting to a near stop before braking gently.

Modern engines may not even be burning fuel during deceleration, as fuel injection suspends until certain preset revolutions are obtained, when it resumes so the engine may idle, not stop.

But having accelerated to a speed, and then used braking to stop, the excess fuel (energy) used is dissipated by the brakes, as heat. The extra energy (fuel) you have wasted is not recoverable, it is heat in the brakes, and dissipated to the air.

So, gentle acceleration to a constant speed, and gentle deceleration without using brakes except to finally stop, is the most economical way to drive.

Yes, but the problem is that there is air resistance. This is the force exerted by the air on the car as its moving. The faster the car is moving the greater the resistance force so a car traveling at 40 mph uses more fuel than a car traveling 30 mph even if they travel the same distance.

The forces which are allowed to decelerate the car (bearing friction, atmospheric drag, rolling resistance of tires, etc) must be reversed upon acceleration, which is provided by the power generated by the engine.

Maintaining a constant velocity requires less work than accelerating from a lower velocity.

Put another way: the force needed for acceleration is greater than the force needed for maintenance of velocity.

So, recovering a previous velocity (accelerating) uses more fuel than "cruising at speed".

From an Inertia standpoint: overcoming the inertia of a vehicle at rest (or any velocity lower than desired) requires more force than "maintaining" an inertia.

An automobile at low velocity produces less "favorable" inertia than a vehicle at higher velocities (yet not moving fast enough to experience opposing forces from air resistance).

[Inertial] Force = Mass x Velocity The faster the car is going, the greater its inertia. The greater a car's inertia, the less force you have to apply to move (keep moving) the car.

While I'm being long-winded: Notice that a disabled car is easier to push (by hand) once you get it moving? Getting it rolling is where all of the grunting comes in, but once it is rolling, you can relax a little.

A prime example of the force of inertia is the difficulty in STOPPING (engines at full reverse) a large, sea-going, oil tanker. The supertanker has such a tremendous force of inertia that it may take a mile to get it stopped from a speed of only 18 miles per hour. Slowing the oil-tanker, and speeding up your car, are BOTH examples of acceleration. BOTH require more overcoming force than maintaining a constant speed.

Maintaining an inertia is easier (requires less force) than overcoming an inertia.

Getting the car up to speed from a dead start means accelerating it, which means applying a force over a distance, which means doing work on the car, expending an amount of energy. It doesn't matter how far it travels at that ultimate speed; it takes the same amount of work to bring it up to that speed.

According to the Work-Energy Theorum, any change in kinetic energy is work, and work is energy. Therefore, if your velocity is constant, your kinetic energy is not changing, and you're doing no work, so requiring no energy. If you speed up or slow down, your kinetic energy is changing, which requires work, which is energy.

you know how hot brakes can get when they're frictating. that right there is wasted energy. or imagine you're pushing a car down the road. you get it rolling...you got 40 yards to go and the guy brakes...grrr...you push hard and get it rolling again and the guy brakes... sure u may finally get there but he sure made it a lot harder.