Questions: An object travels east for 500 m at a speed of 25 m / s and then west for 800 m at 16 m / s. a. What was the distance traveled by the object? (1300 m) b. What was the final displacement of the object? (300 m west) c. What was the average speed of the object? (18.6 m / s)

Solution Steps

The total distance traveled by the object is the sum of the distances traveled in each direction. The object travels 500 m east and 800 m west.

\[ \text{Total distance} = 500 \, \text{m} + 800 \, \text{m} = 1300 \, \text{m} \]

Displacement is the difference between the final and initial positions, taking direction into account. The object travels 500 m east and then 800 m west. The net displacement is:

\[ \text{Displacement} = 800 \, \text{m (west)} - 500 \, \text{m (east)} = 300 \, \text{m (west)} \]

Average speed is the total distance traveled divided by the total time taken. First, calculate the time taken for each segment of the journey:

• Time to travel 500 m east at 25 m/s: \[ t_1 = \frac{500 \, \text{m}}{25 \, \text{m/s}} = 20 \, \text{s} \]

• Time to travel 800 m west at 16 m/s: \[ t_2 = \frac{800 \, \text{m}}{16 \, \text{m/s}} = 50 \, \text{s} \]

The total time is: \[ \text{Total time} = t_1 + t_2 = 20 \, \text{s} + 50 \, \text{s} = 70 \, \text{s} \]

The average speed is: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{1300 \, \text{m}}{70 \, \text{s}} \approx 18.5714 \, \text{m/s} \]

Rounding to four significant figures, the average speed is \(18.57 \, \text{m/s}\).

Final Answer