QuestionAugust 18, 2025

4. A car travels 12.0 km east in 10.0 min, then 8.0 km west in 6.0 min. a) Find the total distance traveled. b) Find the displacement. c) Find the average velocity for the trip.

4. A car travels 12.0 km east in 10.0 min, then 8.0 km west in 6.0 min. a) Find the total distance traveled. b) Find the displacement. c) Find the average velocity for the trip.
4. A car travels 12.0 km east in 10.0 min, then 8.0 km west in 6.0 min.
a) Find the total distance traveled.
b) Find the displacement.
c) Find the average velocity for the trip.

Solution
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Answer

a) Total distance traveled: 20.0 km ### b) Displacement: 4.0 km east ### c) Average velocity: 15.0 km/hr east Explanation 1. Calculate Total Distance Add the distances traveled in each direction: 12.0 \, \text{km} + 8.0 \, \text{km} = 20.0 \, \text{km}. 2. Calculate Displacement Subtract the westward distance from the eastward distance: 12.0 \, \text{km} - 8.0 \, \text{km} = 4.0 \, \text{km} east. 3. Calculate Total Time Add the time taken for each segment: 10.0 \, \text{min} + 6.0 \, \text{min} = 16.0 \, \text{min}. 4. Convert Time to Hours Convert minutes to hours: 16.0 \, \text{min} \times \frac{1 \, \text{hr}}{60 \, \text{min}} = 0.267 \, \text{hr}. 5. Calculate Average Velocity Use the formula for average velocity: \text{Average velocity} = \frac{\text{Displacement}}{\text{Total time}} = \frac{4.0 \, \text{km}}{0.267 \, \text{hr}} \approx 15.0 \, \text{km/hr} east.

Explanation

1. Calculate Total Distance<br /> Add the distances traveled in each direction: $12.0 \, \text{km} + 8.0 \, \text{km} = 20.0 \, \text{km}$.<br /><br />2. Calculate Displacement<br /> Subtract the westward distance from the eastward distance: $12.0 \, \text{km} - 8.0 \, \text{km} = 4.0 \, \text{km}$ east.<br /><br />3. Calculate Total Time<br /> Add the time taken for each segment: $10.0 \, \text{min} + 6.0 \, \text{min} = 16.0 \, \text{min}$.<br /><br />4. Convert Time to Hours<br /> Convert minutes to hours: $16.0 \, \text{min} \times \frac{1 \, \text{hr}}{60 \, \text{min}} = 0.267 \, \text{hr}$.<br /><br />5. Calculate Average Velocity<br /> Use the formula for average velocity: $\text{Average velocity} = \frac{\text{Displacement}}{\text{Total time}} = \frac{4.0 \, \text{km}}{0.267 \, \text{hr}} \approx 15.0 \, \text{km/hr}$ east.
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