A car travels along a straight stretch of road.
It proceeds for 11.9 mi at 58 mi/h, then
29.4 mi at 44 mi/h, and finally 36.9 mi at
31.6 mi/h.
What is the car’s average velocity during
the entire trip?
Answer in units of mi/h
To find the car's average velocity during the entire trip, we need to calculate the total displacement and total time taken.
1. Firstly, find the displacement for each segment of the trip. Displacement is the change in position and can be calculated by subtracting the initial position from the final position.
- For the first segment, the displacement is 11.9 mi.
- For the second segment, the displacement is 29.4 mi.
- For the third segment, the displacement is 36.9 mi.
2. Next, calculate the total displacement. Add up all the individual displacements:
Total Displacement = 11.9 mi + 29.4 mi + 36.9 mi = 78.2 mi
3. Now, determine the total time taken for the entire trip. Divide the distance traveled in each segment by the respective speed to find the time taken for each segment, and then add them together.
- For the first segment, time = distance / speed = 11.9 mi / 58 mi/h = 0.2052 h
- For the second segment, time = distance / speed = 29.4 mi / 44 mi/h = 0.6682 h
- For the third segment, time = distance / speed = 36.9 mi / 31.6 mi/h = 1.1677 h
Total Time = 0.2052 h + 0.6682 h + 1.1677 h = 2.0411 h
4. Finally, calculate the average velocity by dividing the total displacement by the total time:
Average Velocity = Total Displacement / Total Time = 78.2 mi / 2.0411 h ≈ 38.29 mi/h
Therefore, the car's average velocity during the entire trip is approximately 38.29 mi/h.