The energy it takes to accelerate or decelerate is dependent on how fast you are going. It takes a lot more energy to change your speed by say, 10 mph, when you are going fast rather than when you are going slow. A 70-80 mph acceleration takes a lot more energy than a 40-50 mph acceleration, which takes a lot more energy than accelerating from 0-10 mph. The energy needed is proportional to the difference in the SQUARES of the speeds, not the difference in the speeds themselves. Hence, it takes FIFTEEN TIMES more energy to accelerate from 70-80 than from 0-10! Therefore, going between 0 and 15mph many times might not be as impactful as one might think.

**Too much info on the physics behind the calculation**:

This is pretty much a copy of the “Highway Braking Cost Calculator”

30-35% of the gas that your car burns does work to accelerate the car (the rest of the gas goes to useless thermal energy (your engine gets really hot!)). According to the work-energy principle, when neglecting losses to friction, the work done is equal to the change in kinetic energy (KE) of the car. We calculate the change in KE as 0.5*mass*(velocity2^{2} – velocity1^{2}). The calculator converts pounds to kg and speed to m/s so that KE comes out in units of Joules.

To figure out how many gallons of gas is needed to provide those Joules, we must find out how much energy a gallon of gas can provide. I took an average value between those given by two different websites: about 123,400,000 J per gallon. But remember, most of this energy is lost to heat! I assumed that 32.5% of this amount could actually go toward providing kinetic energy. That would be about 40,000,000 J. To find gallons of gas used, the calculator just divides gallons used by 40 million.

**Conclusion**

I am guessing that you won’t save enough to make it worth getting traffic tickets and ending up in more fender-benders.