# How much does it cost every time your car stops for a traffic light?

Every time we have to stop the car, it is costing us extra money, because we have to then accelerate to full speed again. I would like to know how much.

In order to simplify the situation, we can make these assumptions.

• we disregard cost of car maintenance (brake pads wearing out etc.). This is focused entirely on fuel economy.
• A car is always traveling at 60km/h when it needs to stop
• The car's fuel economy is 8L/100kms when traveling at 60km
• The cost of fuel is \$1.25 per litre.
• The car weighs 1000kg

I will be happy with either a definitive answer, an explanation of how to arrive at the answer, or an explanation of why there is not enough information in the question to come up with the answer.

• Off topic. Some vehicle brake system may connected to a engine to generate electricity and it is used later for acceleration, so the cost is small in those vehicle :) – unsym Dec 17 '10 at 12:32
• The crucial parameter is how your fuel consumption depends on the acceleration (and rpm) because the major part of your cost is due to a much lower efficiency of accelerating car compared to a car traveling at a constant speed. – gigacyan Dec 17 '10 at 12:44
• Where do you live that they both charge in dollars and measure in liters? – Mark Eichenlaub Dec 17 '10 at 21:03
• @Mark : australia. – RoboShop Dec 18 '10 at 11:41
• It depends on whether or not you ran the light first and got a ticket:) – Gordon Feb 3 '11 at 5:19

The kinetic energy of a 1000 kg car moving at 60 km/h is $$E=\frac{mv^{2}}{2}=\frac{1000kg(16.7m/s)^{2}}{2}=138.9 kJ$$
The heat of gasoline combustion is 47 MJ/kg = 35000 kJ/litre. Assuming 10% efficiency of the car's engine, you would need to burn $$\frac{138.9 kJ}{0.1\cdot35000kJ/l}=0.04 litre$$ of gasoline to accelerate the car to a given speed which would cost you 5 cents.