The whole scenario seems to be implausible when you consider that in order for the person to accelerate the vehicle to a speed of 30 m/s at the end the person would have to run at a pace of 70 mph!

As to the food calories burned:

According to one site an average person's straight pushing force is 60-80 N. Assuming 80 N and a 1000 kg car (2200 lb), which is a fairly light compared to the average, and negligible friction between the car and road, the car's acceleration would be 0.08$\frac{m}{s^2}$. That means it would take 6.26 minutes to reach 30 m/s and do 450 kJ of mechanical work.

Another site mentioned that human energy efficiency in converting food energy into mechanical output is about 25%. So the required food energy would be 450/.25, or 1800 kJ.

Hope this helps.

The whole scenario seems to be implausible when you consider that in order for the person to accelerate the vehicle to a speed of 30 m/s at the end the person would have to run at a pace of 70 mph!

A more reasonable speed to push the car is about 10 mph or 4.5 m/s which is a kinetic energy of about 10 kJ. That’s only 10% of your hamburger’s calories.

By the way, according to one site an average person's straight pushing force is 60-80 N. At 80 N assuming negligible friction the car's acceleration would be 0.08$\frac{m}{s^2}$. So If would take about a minute to reach 4.5 m/s.

Hope this helps.