If you think about what the car is doing in both cases you'll see why you burn more fuel when accelerating.

General theory

F = mA (Force is equal to mass times acceleration), and in this case the force is applied by the engine. The more force, the more fuel is burned.

Acceleration

In stop and go traffic, you are making frequent stops, and accelerating from zero to some relativly low speed, like 30 MPH. Per the above equation, (F=mA) you must have a force in the direction you want to accelerate the mass of your car. But that's a net force. You have the force of the engine moving you forward, but you are being resisted by inertia, friction, and at some point even the air resists your attempt to accelerate. The engine must overcome all of these forces by applying a bigger one. More force is more gas burned.

Highway coasting

While coasting on the highway you are maintaining an acceleration of zero. So the net force applied is zero. So, you only have to match, not exceed like when accelerating, the forces of friction and aerodynamic drag. Less force, means less gas burned.

I hope that helps!

每次剎車，能量都浪費了。制動器通過摩擦將行駛中的汽車的機械能轉化為熱量（它們會加熱）。這是能量最終“丟失”的地方。然後，當交通稍微向前移動時，您當然需要加速-這就是您實際使用油箱中的氣體將這種能量用於使汽車行駛的地方。

當您在恆定速度下，唯一的大能量損失來自空氣阻力。這種阻力取決於汽車的速度和形狀，因此在中等速度（例如55mph）和現代的空氣動力學汽車中，與在交通擁堵中反複製動相比，您實際上損失的能量更少。當然，如果您的汽車的空氣動力學性能較差（例如，在車頂上載有大行李）或駕駛得非常快，那麼最終您將達到比慣性交通擁堵燃燒更多的燃料。

（我跳過了橡膠輪胎的能量損失，因為它們基本保持不變。此外，如果您可以在10分鐘內滑行，但在果醬中呆了整整一個小時，則有很多空轉-但是空轉並不像剎車那樣重要。

這也解釋了為什麼帶電動機的車輛在這種起停交通時效率更高-與其進行常規（摩擦）制動，不如進行“再生製動”，並將部分能量重新帶回電池。

Your engine is always burning gas when the car is running.

When you're stationary, you are burning gas to keep your engine running, without actually moving the car, so you're actual miles per gallon (MPG) at that moment is 0.

When you begin to accelerate, you are using more gas than when the car was idling, but then you have to press the brakes, essentially wasting the extra gas you just used to get up to speed.

Once you're up to speed and no longer accelerating on the highway, the engine is only using 20-40 horsepower to maintain that speed. When you're cruising at 60 mph you're covering mile a minute, so depending on the car, your relative fuel consumption is much higher.

The graph below displays the Brake Specific Fuel Consumption (BSFC - brake specific meaning the engine was mounted on a certain style of engine dyno, rather than in a car). The fuel consumption is measured in grams per kilowatt-hour (1 KWH = 1.34 horsepower). The maximum torque vs RPM (engine Revolutions Per Minute) is displayed at the top of the graph (black line w/ black dots). As you can see, least amount of fuel per KWH is used when THIS engine is running at 2-3k RPM, and outputting 80% of max torque.

Again, when cruising, you only need a fraction of your total horsepower. The engine rpm for most cars in top gear at highway speeds is usually 2500-3500 RPM, so even as your torque requirement goes down and you fall out of the optimum fuel efficiency range, when the value of the denominator (power needed to cruise at 60) decreases, as does the numerator (amount of fuel used).

The most important aspect of the answer to this question is found in Newton's first law of motion:

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

This is the same reason that space shuttle use something like 90% of their fuel on take-off.

As cdunn went into, it's all about force (F). More fuel/s = more force/s.

The key to understanding it is that little snippet "unless acted upon by an unbalanced force."

In the case of your example of a highway with ups and downs, gravity comes greatly into play. On the decline g becomes a positive force. To illustrate clearly I'll use extremes.

Say your decline is 90 degrees, or vertical. That means that g (10m/s^2) is added to the power of your engine. This is why vehicles have intentional methods of engine breaking and drag in various parts - so you don't just blast down hills.Conversely, when traveling back up this Gravity is now a negative force on your engine. So you either need to produce more force from the engine, or produce more force via inertia.

Extreme Example

Say the following is true:    motor output (Mo)= 250 HP or ~ 19,020 kg-m/s^2    curb weight (cw)= ~1800 kg    g = 10m/s^2 • cw = ~18,000 kg-m/s^2    friction = 0    surface resistance = 0Using -- t=(v-v0)/a -- we get the following.In this case nothing is in play exceptgravity and motor output. Whichmeans that in a dead fall you have ~37,020 m/s^2 for and in a vertical incline only ~1,020 m/s^2. So on the decline it only takes 0.00075 seconds for the car to reach100 km/h. Whereas on the incline, it takes 0.0272 seconds to reach the same speed.

While this may not look like much, you can see it's a huge difference.

True that attempting to maintain a constant speed where there are hills is not the most efficient (I cut how most cruise controls systems handle hills). But on flats it is. The trick with hills is to equalize your forces. Getting to a proper speed on a down hill will allow your inertia to carry your farther up hill without massive input from your motor.

But hills aside - you initial question is "why does stopping and starting in traffic burn more fuel." The answer to that is simply because of inertia. But! There are additional actors as well. For example, sitting stopped. Your motor is burning fuel and you are not traveling. So your not really getting 0 MPG, but more like -x MPG because it brings the overall MPG of your trip or count down to eventual 0 or even a negative ratio (e.g. 15 Gal./1 Mile).

Variables like wind resistance, drag, inefficiencies and gravity don't even really come into play until there flowing traffic.

任何引擎都無法達到100％的效率；總是有能量損耗。在這種情況下，您的能量損失是由於氣動阻力，輪胎滾動以及發動機和變速箱的摩擦造成的。請注意，前兩種方式與速度的平方成正比，變速器的損耗與速度成正比，發動機的摩擦力與實際的RPM成正比。

當卡在交通擁堵時，通常前兩個檔位只會降低阻力大，但發動機摩擦力更大，並且發動機可在各種RPM下運行。當您制動停止時，從燃料中獲得的所有動能都被浪費掉了。當您繼續使用發動機時，您浪費燃油只是為了保持發動機啟動。如果加速，則燃燒更多的燃料以提高動能；如果換檔太早或太晚，則僅由於發動機超出其最佳RPM範圍而燃燒了額外的燃料。從暫停開始時，您必須將離合器打滑一會兒。

即使您不完全停止制動（浪費動能），您也確實使用了發動機制動，您使用了起停功能，在正確的時間轉移；巡航智能方式時無法達到燃油經濟性。

Another way to view this is to visualise throttle opening.

When you're cruising, the pedal is held down to some position more than idle, but less than maximum

When you're taking off and accelerating, the pedal is pressed down further, which opens the butterfly valve allowing more fuel/air mixture into the engine.

Hence more fuel is used to accelerate than to cruise.

Yes I realise answer is fudging, modern cars, computers, injection etc - handwave and simply

Separately, idling uses fuel for no progress, which is why some cars shut off their engine at a dead stop. As a cyclist it sounds so strange at the green light, to hear three or four cars all turn over their engines at once.

Simple answer: fuel burn at cruising (at a steady 55 mph) is proportional to the friction (aerodynamic \ tire \ mechanical bearings). High transient driving (stop-and-go with conventional friction braking) energy consumption is significantly higher than energy burn due to steady-state friction. Hybrid electric braking is energy conservative and should be thought of as a special case.

Wear and tear on the engine / tires / brakes are also pronounced in cars that are driven in stop-and-go roads.

簡單地說：加速會消耗能量。制動不會為您贏得任何能量（至少在您的普通汽車中）。

因此，如果方案1涉及加速和製動，而方案2涉及以恆定速度進行的穩定巡航，則方案1會花費更多能量（燃料），僅僅是因為您花費了燃料來加速。並不是剎車本身就很糟糕，但是剎車告訴您，您可以避免加速，從而節省了加速燃油的消耗。

附錄：有一種情況3：在適當的檔位，盡可能快地加速至目標速度，然後鬆開離合器，使電動機空轉。這比方案2所用的燃料更少，因為在較高的RPM時，普通電動機會更高效（一定程度上，請勿將油門踏板一直踩到底，因為現代電動機會隨後泵入額外的燃料以提供給您一種“加力”效果）。

這需要一些正確的練習，即，您必須加速到足夠高的速度，才能獲得有意義的滾動時間，同時又不違反速度限制並且不妨礙其他賽車；如果您仍然必須在滾動結束時剎車，這對您並沒有真正的好處。因此，我不建議新手這樣做，但是經驗豐富的駕駛員可以從中節省一些燃油。谷歌“超級微笑”。

此外，通常，嘗試用電動機而不是製動器製動（如果安全允許的話），顯然，因此電動機將使用0燃料（而不是微小的怠速燃料） ）。

One reason is that fossil fuel engines are tuned to run most efficiently around 50-60mph, so any other speed will not deliver as much torque for the fuel being burned - that's why cruising speed is where it is.

Another, which I will focus on, is that regardless of what speed you travel at, every time you brake, you waste energy. Here's what it looks like if you accelerate and then take your foot off the accelerator:

Here's what it looks like if you hit the brakes:

And a comparison:

Thus any time you brake, you haven't gone as far as you could've - you've spent fuel up front in accelerating that could've taken you further. You now have to spend energy again to cover that distance.

Here's what that looks like in traffic - notice the accumulation of wasted energy:

Verses the waste if you just brake once at the end:

Incidentally, this is one problem hybrid cars address: when you hit the brakes, they use induction to recharge the battery, and there's less waste.

我認為我們可以簡單地以最簡單的方式引用牛頓的第一運動定律來回答這個問題。

牛頓的第一運動定律：I.每個物體都處於一個狀態除非施加外力，否則勻速運動趨於保持在該運動狀態。我們本質上認為這是伽利略的慣性概念，通常簡稱為“慣性法”。

當我們考慮將其應用於汽車時，汽車會沿著平坦的平面滑行除非有力作用在表面上，否則表面將繼續以相同的速度運行。 （在此示例中，忽略了沿道路滾動的阻力和摩擦力。）

對於靜止的車輛，您需要燃燒燃料以產生作用在汽車及其零部件（發動機零部件，驅動軸，

使用制動器在汽車上施加強大的摩擦力，將汽車的慣性（動能）轉化為熱量。

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在正在起停的汽車中，您燃燒了更多的燃料，因為您失去了作為廢熱而停止的動能，然後不得不花費燃料中的能量來再次增加車輛及其部件的慣性

因此，要停止行駛的汽車會消耗更多的燃料。

我認為在高速公路上停走要比在高速公路上行駛時消耗更少的燃料。

請考慮以下使用典型高速公路和走走停停的速度情況，和這些速度下的逼真的MPG。您可以看到汽車在高速公路上燃燒的燃料比在走走停停的交通中更快。