Kinematics - identifying and describing types of motion

1. Mar 22, 2016

alexandria

1. The problem statement, all variables and given/known data
I'm really having a hard time with this question, i posted the same question on another forum, but didn't really understand what the teacher was trying to say, please explain for me.
thank you :)

a) Calculate the time per mode of transport of the lettuce from each starting point.
b) calculate the total time required for each complete journey of the lettuce from its origin to Barrie

c)

d)

e)

2. Relevant equations
time = distance / speed or t = d/v

3. The attempt at a solution

a) and b)
- for a) to calculate time per mode of transport, i divided the partial distances by the average speed
- for b) to calculate the total time i added the time per mode of transport
please tell me if this is correct.

c) i dont understand what to do here. Do they want me to determine the carbon dioxide emissions for each route, as in the truck, train and plane portions, or the average carbon dioxide emissions. And how would i do that?

d) ***

Route 1. Fuel consumed = (31 km) x (30 L / 100 km) = 9.3 L

Route 2. Fuel consumed = (63 km) x (1.2 L / 100 km) = 0.76 L

Route 3. Fuel consumed = (81 km) x (30 L / 100 km) = 24 L

Route 4. Fuel consumed = (2279 km) x (3.5 L / 100 km) = 80 L

Route 5. Fuel consumed = (81 km) x (30 L / 100 km) = 24 L

e) ***
please tell me if im right here.
Considering that each shipment of lettuce is priced at the same value, I would chose to purchase the lettuce
that travels the least distance (which would be the first route of lettuce). Since the lettuce travels less distance, the lettuce would be fresher, and of higher quality. It consumes a small amount of fuel (only 9.3 L) and does not produce a great amount of carbon dioxide emissions. Even though Route 2 consumes less fuel (0.76 L), it still has a longer distance to travel, meanin the lettuce will not be as fresh.

Last edited by a moderator: Mar 22, 2016
2. Mar 22, 2016

alexandria

c) ok so i came up with an answer for part c

Route 1: Holland Marsh, Ontario – Barrie, Ontario

Carbon dioxide emissions = 0.01 tonnes

Route 2: Thorold, Ontario – Barrie, Ontario

Carbon dioxide emissions = 0.01 tonnes + 0.01 tonnes = 0.02 tonnes

Route 3: Solano, California – Barrie, Ontario

Carbon dioxide emissions = 1.08 tonnes + 0.01 tonnes = 1.09 tonnes

3. Mar 22, 2016

haruspex

In e), does freshness depend on distance travelled?

4. Mar 22, 2016

alexandria

im pretty sure it does, the longer the distance travelled, the less fresh the food will be. right?
ok so here are my answers for d) and e)
d)

Fuel consumption for each partial route:

Partial Route 1. Fuel consumed = (31 km) x (30 L / 100 km) = 9.3 L

Partial Route 2. Fuel consumed = (63 km) x (1.2 L / 100 km) = 0.76 L

Partial Route 3. Fuel consumed = (81 km) x (30 L / 100 km) = 24 L

Partial Route 4. Fuel consumed = (2279 km) x (3.5 L / 100 km) = 80 L

Partial Route 5. Fuel consumed = (81 km) x (30 L / 100 km) = 24 L

Average fuel consumption for each route:

Route 1. Average fuel consumption = 9.3 L

Route 2. Average fuel consumption = 0.76 L + 24 L = 24.76 L

Route 3. Average fuel consumption = 80 L + 24 L = 104 L

e)

Considering that each shipment of lettuce is priced at the same value; 99 cents, I would chose to purchase the lettuce that travelled from Holland Marsh, Ontario to Barrie, Ontario. In route 1, the lettuce travels the least distance (only 31 km). Because it travels the least distance and is closer to its destination, the lettuce would be fresher and of higher quality. The lettuce is transported in a truck that consumes the least amount of fuel (9.3 L) and produces the least amount of carbon dioxide emissions (0.01 tonnes). This shipment of lettuce requires the least amount of fuel and does not produce a great amount of carbon dioxide emissions, so it is considered cost efficient and environmentally friendly.

5. Mar 22, 2016

alexandria

did i do qts c) correctly?

6. Mar 23, 2016

haruspex

That's the total fuel consumed, not an average consumption rate. Note the units used to describe average consumption for each transport mode in the question.

Please explain how a lettuce knows how far it has been carried.

7. Mar 23, 2016

alexandria

so how would i calculate the average fuel consumption for d)?
i learned about this thing called the 100 mile diet, it talks about food being grown and delivered within 100-mile radius of the consumers table. It states that the food travels less distance, and is more likely to be fresher and of higher quality. Thats why i chose to purchase the lettuce from route 1, cause it travels the least distance.

8. Mar 23, 2016

haruspex

How do you calculate the average fuel consumption of a vehicle?
Yes, more likely to be, but that's a just a correlation. What actually leads to food losing freshness?

9. Mar 24, 2016

alexandria

i already calculated the average fuel consumption for each partial route, so is it wrong to add them together to solve for the average fuel consumption for each route?
could you provide an example of how to calculate the average fuel consumption of a vehicle?

10. Mar 24, 2016

haruspex

No, you calculated the consumption for each route. You were given the average consumption, L/km, for each mode. Note the units, L/km, not L.

11. Mar 24, 2016

alexandria

so they already gave the average fuel conumption for each partial route, would i just combine them together to calculate the average consumption for the three routes.
Route 1. 30 L/100 km
Route 2. 15.6 L/100 km
Route 3. 16.75/100 km

??

12. Mar 24, 2016

haruspex

No, you are calculating those wrongly.
Compare with this question: you drive 1km at 30km/h, 1km at 60km/h. What is your average speed?

13. Mar 24, 2016

alexandria

is it 45 km/h?

14. Mar 24, 2016

haruspex

No. How far did you travel? How long did it take?

15. Mar 25, 2016

alexandria

im really confused, is there a formula to solve for the average fuel consumption, just like theres a formula to solve for the average speed?

16. Mar 25, 2016

Nathanael

The dimensions of "average fuel consumption" are stated as volume per distance, so we can safely interpret the "average fuel consumption" as being the total volume of fuel used divided by the total distance travelled.

You are told what this value is for any trip which is purely by truck, purely by train, or purely by plane. With that information you are asked how to find that value (total volume of fuel per total distance) for a few "mixed trips" (trips which consist of combinations of truck/train/plane).

17. Mar 25, 2016

alexandria

Fuel consumption for each partial route:

Partial Route 1. Fuel consumed = (31 km) x (30 L / 100 km) = 9.3 L

Partial Route 2. Fuel consumed = (63 km) x (1.2 L / 100 km) = 0.76 L

Partial Route 3. Fuel consumed = (81 km) x (30 L / 100 km) = 24 L

Partial Route 4. Fuel consumed = (2279 km) x (3.5 L / 100 km) = 80 L

Partial Route 5. Fuel consumed = (81 km) x (30 L / 100 km) = 24 L

Average fuel consumption for each route: total volume of fuel used/total distance travelled

Route 1. Average fuel consumption = 9.3 L / 31 km = 0.3 L / km

Route 2. Average fuel consumption = 24.76 L / 144 km = 0.172 L/km

Route 3. Average fuel consumption = 104 L / 2360 km = 0.044 L/km

ok i think i got it, what do you think?

18. Mar 25, 2016

Nathanael

Without checking the numbers, it looks correct. Notice the Average Fuel Consumption (AFC) for route 1 (0.3L / km) is the same as is given for the AFC of a truck (30L / 100km). This is because it should be the same for all trips which are purely by one (and the same) mode.

Let us generalize that into a question: If two trips (which may cover different distances) have the same ratio of modes (e.g. 1/2 by truck 1/6 by train 1/3 by plane) then will they have the same AFC? @alexandria

19. Mar 25, 2016

alexandria

if they have the same ratio of modes, but cover different distances, they would not have the same AFC. right?
so did i calculate the average fuel consumption correctly?

20. Mar 25, 2016

Nathanael

Actually, I think they would have the same AFC. Let's try it for an arbitrary trip of distance $\ell$ for the ratio of modes in post #18 (1/2 by truck, 1/6 by train, 1/3 by plane). We would get: $$[AFC]_{trip} = \frac{[AFC]_{truck}\ell/2+[AFC]_{train}\ell/6+[AFC]_{plane}\ell/3}{\ell}=\frac{1}{2}[AFC]_{truck}+\frac{1}{6}[AFC]_{train}+\frac{1}{3}[AFC]_{plane}$$
Notice how $\ell$ cancels out, and so it doesn't matter how far the trip is, it only matters the ratios of the modes.
Anyway I guess this is not important for the problem, but I thought maybe you'd like to see that.

Yes, well done.