A motorist drives south at 26.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.40 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.40 min trip, find the following values.find displacement, average speed, and average velocity
To find the displacement, average speed, and average velocity of the motorist's trip, we will need to break down the given information and calculate each value separately.
1. Displacement:
Displacement refers to the change in position of an object. To find the displacement, we need to determine the net distance travelled in both the x and y directions.
Given:
- Southward distance: 26.0 m/s * 3.00 min = 78.0 m
- Westward distance: 25.0 m/s * 2.40 min = 60.0 m
- Northwestward distance: 30.0 m/s * 1.00 min = 30.0 m
To find the net displacement, we need to use vector addition. Since the motorist first moves in the south direction, then turns west, and finally travels northwest, we can represent these directions using the x and y axes.
Net displacement in the x-direction = westward distance - northwestward distance = 60.0 m - 30.0 m = 30.0 m (towards the west).
Net displacement in the y-direction = southward distance = 78.0 m (towards the south).
Using the Pythagorean theorem, we can calculate the magnitude of the displacement:
Displacement = sqrt((Net displacement in x)^2 + (Net displacement in y)^2)
Displacement = sqrt((30.0 m)^2 + (78.0 m)^2) ≈ 83.0 m
Therefore, the displacement of the motorist is approximately 83.0 m.
2. Average Speed:
Average speed is calculated by dividing the total distance travelled by the total time taken.
Given:
- Southward distance: 78.0 m
- Westward distance: 60.0 m
- Northwestward distance: 30.0 m
- Total time: 6.40 min
Total distance = Southward distance + Westward distance + Northwestward distance
Total distance = 78.0 m + 60.0 m + 30.0 m = 168.0 m
Average speed = Total distance / Total time
Average speed = 168.0 m / 6.40 min ≈ 26.25 m/min
Therefore, the average speed of the motorist is approximately 26.25 m/min.
3. Average Velocity:
Average velocity is calculated by dividing the displacement by the total time taken.
Given:
- Displacement: 83.0 m
- Total time: 6.40 min
Average velocity = Displacement / Total time
Average velocity = 83.0 m / 6.40 min ≈ 12.97 m/min
Therefore, the average velocity of the motorist is approximately 12.97 m/min.