Question

Sally travels by car from one city to another. She drives for 29.0 min at 67.0 km/h, 52.0 min at 46.0 km/h, and 19.0 min at 76.0 km/h, and she spends 9.0 min eating lunch and buying gas.

Answer 1

Answer on Question #46889-Physics-Other

Sally travels by car from one city to another. She drives for 29.0 min at 67.0 km/h, 52.0 min at 46.0 km/h, and 19.0 min at 76.0 km/h, and she spends 9.0 min eating lunch and buying gas. Determine the average speed for the trip.

Solution

Distances traveled are

$$\Delta x _ {1} = v _ {1} \Delta t _ {1} = 67.0 \frac {\mathrm {k m}}{\mathrm {h}} \cdot \frac {29.0}{60} h = 32.4 \mathrm {k m},$$ $$\Delta x _ {2} = v _ {2} \Delta t _ {2} = 46.0 \frac {\mathrm {k m}}{\mathrm {h}} \cdot \frac {52.0}{60} h = 39.9 \mathrm {k m},$$ $$\Delta x _ {3} = v _ {3} \Delta t _ {3} = 76.0 \frac {\mathrm {k m}}{\mathrm {h}} \cdot \frac {19.0}{60} h = 24.1 \mathrm {k m}.$$

Thus, the total distance traveled is $x = \Delta x_{1} + \Delta x_{2} + \Delta x_{3} = 32.4 \, \text{km} + 39.9 \, \text{km} + 24.1 \, \text{km} = 96.4 \, \text{km}$, and the elapsed time is $\Delta t = \frac{29.0 + 52.0 + 19.0 + 9.0}{60} = 1.8 \, \text{h}$.

The average speed for the trip is

$$\bar {v} = \frac {\Delta x}{\Delta t} = \frac {96.4 \, \text{km}}{1.8 \, \text{h}} = 53.6 \, \frac {\text{km}}{\text{h}}.$$

Answer: $53.6 \, \frac{\text{km}}{\text{h}}$.

http://www.AssignmentExpert.com/