It is 5.0 km from your home to the Physics lab and your car is out of gas. You could run that distance

at 10 km/h, which uses up energy at the rate of 700 W; or you could walk it leisurely at 3.0 km/h,
which uses energy at 300 W.
(a) Calculate how much energy both choices would burn up.
(b) The conversion between energy units is: 1 Cal (food calaorie) = 1 kcal (kilocalorie) = 1000 cal
(thermochemical calorie) = 4184 J (joules). Calculate how much energy both choices would burn
up in units of J, cal and Cal.
(c) Which choice would burn up more energy?

Can someone help me figure out what formula to use!!

10 km/hr = 10/3.6 = 2.78 m/s

3 km/hr = 3/3.6 = .833 m/s

5 km at 10 km/hr --> 30 min which is 30 *60 = 1800 s
energy = 700*1800 = 1.26*10^6 Joules

5 km at 3 km/hr --> 6,000 s

6,000 s * 300 w = 1.8*10^6 Joules

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(a) To calculate the amount of energy burned up, we can use the formula:

Energy = Power x Time

For running:
Energy (running) = Power (running) x Time (running)

Given:
Power (running) = 700 W
Time (running) = Distance / Speed = 5.0 km / 10 km/h = 0.5 h

Energy (running) = 700 W x 0.5 h = 350 Wh

For walking:
Energy (walking) = Power (walking) x Time (walking)

Given:
Power (walking) = 300 W
Time (walking) = Distance / Speed = 5.0 km / 3.0 km/h = 1.67 h (approx.)

Energy (walking) = 300 W x 1.67 h ≈ 501 Wh

(b) To convert the energy units, we can use the given conversion factors:
1 Calorie (Cal) = 1 kilocalorie (kcal) = 1000 calories (cal) = 4184 joules (J)

Converting energy burned up in running:
350 Wh x 1000 cal/Wh = 350,000 cal
350 Wh x 4184 J/Wh = 1,461,400 J
350 Wh / 1 kcal = 350 kcal
350 Wh / 1 Cal = 0.35 Cal

Converting energy burned up in walking:
501 Wh x 1000 cal/Wh = 501,000 cal
501 Wh x 4184 J/Wh = 2,091,684 J
501 Wh / 1 kcal = 501 kcal
501 Wh / 1 Cal = 0.501 Cal

(c) From the calculations, we can see that walking would burn up more energy. The energy burned up in walking is greater than the energy burned up in running.

To calculate the energy burned up by both choices, we can use the formula:

Energy (in joules) = Power (in watts) * Time (in seconds)

(a) Let's calculate the energy burned up by running and walking:

Running:
Power = 700 watts (given)
Time = Distance/Speed = 5.0 km / 10 km/h = 0.5 hours = 1800 seconds

Energy (running) = 700 watts * 1800 seconds = 1,260,000 joules

Walking:
Power = 300 watts (given)
Time = Distance/Speed = 5.0 km / 3.0 km/h = 1.67 hours = 6,012 seconds

Energy (walking) = 300 watts * 6,012 seconds = 1,803,600 joules

(b) To convert the energy into different units, we can use the conversion factors:

1 Cal = 1000 cal = 4184 J

Energy (running) = 1,260,000 joules = 1,260,000 / 4184 = 300.96 Cal = 300,960 cal
Energy (walking) = 1,803,600 joules = 1,803,600 / 4184 = 431.32 Cal = 431,320 cal

(c) Comparing the energy burned up:

Energy (running) = 300.96 Cal
Energy (walking) = 431.32 Cal

Since walking burns up more energy than running, walking would require more energy to cover the distance.