Is my driving efficient?

Classical Mechanics Level 3

The fuel efficiency of a car is represented by the distance in kilometers it can run with one liter of fuel (or miles per gallon in the United States). It is well known that the fuel efficiency varies substantially according to the driver's driving habits.

Cindy is driving her Camry at 36 km/h on a straight road, when she spots a traffic light turn red 75 meters ahead. She decelerates at a constant rate, and 6 seconds later she stops right at the traffic light. She waits 2 minutes for the light to turn green, and then accelerates at a steady rate of $2\text{ m/s}^2$ until she reaches her previous speed of 36 km/h. Then she cruises at a steady speed for 2 kilometers. Approximately what is her overall fuel efficiency in kilometers per liter? Round your answer to the nearest integer.

Details and Assumptions

The fuel consumption rate when decelerating or staying still at the red light is 20 ml/min.
The fuel consumption rate when driving at a steady speed is 30 ml/min.
The fuel consumption rate when accelerating at $2\text{ m/s}^2$ is 1.2 ml/s.
Ignore any air resistance.
The given measures do not exactly represent the actual performance of a Camry.

The answer is 14.

2 solutions

Ajit Athle
Jun 8, 2015

Using Newton's Laws, we can determine that the deceleration phase lasts 15 secs; hence fuel consumed in this period=5 ml. During waiting another 40 ml is wasted while in the acceleration phase, which lasts 5 secs, the car needs 6 ml of fuel. Finally during cruising for 2 kms another 100 ml is required. Thus, total distance covered =2.1 km using 0.151 litres of fuel which gives us fuel efficiency as 13.91 km/lit or about 14 km/lit to the nearest integer. So to answer your question, I'd say that your driving is quite efficient considering the engine capacity of the car.

Thanks for the nice solution! Though the problem states that the deceleration phase lasts 6 secs instead of 15; but no big deal on that

Aditya Virani Staff - 6 years ago

Adrian Peasey
Jun 29, 2015

First consider the fuel used in each section:

Decelerating/stationary time is 2.1 minutes, meaning 42ml was used.

Accelerating time can be found by converting 36km/h to 10m/s, giving 5 seconds so 6ml was used.

Cruising time is 2/36 hours or 10/3 minutes, meaning 100ml was used.

This gives a total of 148ml.

Now consider the total distance travelled:

Decelerating covered 75m.

Accelerating can be found using $s=\frac{1}{2}at^2$ to be 25m.

Cruising covered 2km or 2000m.

This gives a total of 2100m travelled.

So the efficiency in km/l is given by $\frac{2100}{148}=14.189...\approx\boxed{14}$ .

Is my driving efficient?

The answer is 14.

2 solutions

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