Position, distance and displacement Transitional Reasoning Download PDF

Questions

1. 1.

   An automated guided cart in a hospital corridor moves along a straight track aligned with a coordinate axis where the forward direction is positive. Starting from an initial position of $+20\text{ m}$, the cart travels forward to an unrecorded delivery station, reverses direction to move $35\text{ m}$ backward, and finally advances $15\text{ m}$ forward to dock at $+70\text{ m}$. What are the cart's net displacement from its starting position and the total distance it traveled during the entire run?

   • A) Net displacement: $+50\text{ m}$; Total distance: $100\text{ m}$
   • B) Net displacement: $+50\text{ m}$; Total distance: $120\text{ m}$
   • C) Net displacement: $+70\text{ m}$; Total distance: $120\text{ m}$
   • D) Net displacement: $+50\text{ m}$; Total distance: $70\text{ m}$
2. 2.

   A wildlife tracking team navigates through dense woodland in two successive straight-line segments. The team first walks a distance of 12 km and then, after resting, walks an additional distance of 5 km in an unspecified direction. Which statement correctly identifies the total distance traveled by the team and the mathematically possible range for the magnitude of their net displacement from the starting point?

   • A) The total distance traveled is 17 km, and the magnitude of the net displacement must be exactly 13 km.
   • B) The total distance traveled can range from 7 km to 17 km, while the magnitude of the net displacement is strictly 17 km.
   • C) The total distance traveled is 17 km, and the magnitude of the net displacement can range from 0 km to 17 km.
   • D) The total distance traveled is 17 km, and the magnitude of the net displacement can range from 7 km to 17 km.
3. 3.

   An automated testing rover drives along a flat proving track shaped like a stadium oval with two straight, parallel east-west lanes connected by semicircular curves of radius 30 m. Starting at the western end of the southern lane (Point P), the rover travels 80 m due east along this lane and then continues counterclockwise along the eastern semicircular bend to reach Point Q at the eastern end of the northern lane. What are the total distance traveled by the rover and the magnitude of its net displacement from Point P to Point Q? (Take $\pi = 3.14$.)

   • A) Total distance: 174.2 m; Net displacement magnitude: 100 m
   • B) Total distance: 174.2 m; Net displacement magnitude: 60 m
   • C) Total distance: 174.2 m; Net displacement magnitude: 140 m
   • D) Total distance: 268.4 m; Net displacement magnitude: 100 m
4. 4.

   At a maritime terminal, a crane moves a shipping container across a vertical coordinate plane where the positive x-axis points horizontally east and the positive y-axis points vertically upward. The container, initially at rest on a transport trailer at (15 m, 4 m), is hoisted vertically to an elevation of 20 m to clear a barrier, shifted horizontally east to x = 27 m at that elevation, and finally lowered vertically onto a cargo vessel deck at (27 m, 9 m). What are the total distance traveled by the container and the magnitude of its net displacement during this entire operation?

   • A) Total distance: 39 m; Magnitude of net displacement: 13 m
   • B) Total distance: 39 m; Magnitude of net displacement: 17 m
   • C) Total distance: 28 m; Magnitude of net displacement: 13 m
   • D) Total distance: 17 m; Magnitude of net displacement: 13 m
5. 5.

   An autonomous ground vehicle conducts an environmental survey across a field grid whose origin (0 m, 0 m) is a central base station. The vehicle starts from an initial waypoint at (-18 m, 25 m) and navigates along a winding path around obstacles to reach a sampling site at (30 m, -11 m). If the vehicle's onboard odometer records a total distance of 78 m for this trip, what are the magnitude of its net displacement and the difference between the distance traveled and this displacement magnitude?

   • A) Magnitude of displacement: 84 m; Difference: 6 m
   • B) Magnitude of displacement: 78 m; Difference: 0 m
   • C) Magnitude of displacement: 50 m; Difference: 28 m
   • D) Magnitude of displacement: 60 m; Difference: 18 m
6. 6.

   A cross-country runner starts a workout at a park pavilion, which serves as the reference origin. The runner jogs 500 m due east along a straight trail to a trail junction, then turns due south and jogs 1200 m along another straight path to a scenic overlook. From the overlook, the runner follows a straight connector trail leading directly back toward the pavilion, jogging 800 m along this trail before stopping to rest. What are the runner's total distance traveled and the magnitude of the net displacement from the pavilion to the resting point?

   • A) Distance: 2500 m; Displacement magnitude: 1300 m
   • B) Distance: 2500 m; Displacement magnitude: 500 m
   • C) Distance: 2500 m; Displacement magnitude: 900 m
   • D) Distance: 1700 m; Displacement magnitude: 500 m
7. 7.

   An automated surveillance drone patrols the perimeter of an equilateral triangular conservation area whose corners are designated as Station 1, Station 2, and Station 3, with each straight side measuring 200 m. The drone launches from Station 1, flies along the boundary to Station 2, continues along the boundary to Station 3, and then flies halfway along the final side back toward Station 1 before landing at a field research post. What are the total distance traveled by the drone and the magnitude of its net displacement from Station 1 to the research post?

   • A) Total distance: 500 m; magnitude of displacement: 100 m
   • B) Total distance: 500 m; magnitude of displacement: 300 m
   • C) Total distance: 300 m; magnitude of displacement: 100 m
   • D) Total distance: 500 m; magnitude of displacement: 500 m
8. 8.

   An environmental monitoring drone takes off from a launchpad at ground level, defined as the coordinate origin (0 m, 0 m, 0 m). To sample air quality above an industrial facility, the drone flies 40 m due east, turns to fly 30 m due north, and then climbs straight up to an altitude of 120 m, where it hovers at its designated sampling station. What are the total distance traveled by the drone and the magnitude of its net displacement from the launchpad to the sampling station?

   • A) Distance = 190 m; Displacement magnitude = 130 m
   • B) Distance = 190 m; Displacement magnitude = 50 m
   • C) Distance = 190 m; Displacement magnitude = 170 m
   • D) Distance = 130 m; Displacement magnitude = 190 m
9. 9.

   An autonomous pipeline inspection gauge traverses an S-shaped bypass pipe composed of two identical connected semicircular sections, each having a radius of 10 m. The gauge enters the first semicircular bend at point P, travels along the curved centerline of both bends without reversing, and exits the second bend at point Q, which lies along the same straight axis as point P. What are the total distance traveled by the gauge and the magnitude of its net displacement from point P to point Q? (Take $\pi = 3.14$.)

   • A) Total distance = 40 m; Displacement magnitude = 40 m
   • B) Total distance = 62.8 m; Displacement magnitude = 20 m
   • C) Total distance = 62.8 m; Displacement magnitude = 40 m
   • D) Total distance = 31.4 m; Displacement magnitude = 40 m
10. 10.

    During a diagnostic run along a straight east-west track, an automated inspection cart starts at position -5 m and travels a total distance of 22 m before stopping at position +7 m. An engineering student analyzes this telemetry log to determine the cart's net displacement and evaluate whether it reversed direction during the trial. Which statement correctly identifies the cart's net displacement and provides the valid deduction about its motion?

    • A) The net displacement is +17 m, and the cart traveled continuously eastward without reversing direction.
    • B) The net displacement is -12 m, and because the displacement is negative, the cart moved only westward.
    • C) The net displacement is +12 m, and because the net displacement is positive, the cart never changed its direction of motion.
    • D) The net displacement is +12 m, and because the total distance traveled (22 m) exceeds the magnitude of its net displacement (12 m), the cart must have reversed direction during the run.
11. 11.

    A coastal survey vessel departs from an offshore buoy located at coordinates $(10\text{ km}, 10\text{ km})$ on a navigation grid whose origin $(0, 0)$ is the harbor control tower. The vessel sails along a straight path to an oceanographic station at $(50\text{ km}, 40\text{ km})$, and after taking water samples, it sails due south in a straight line to a supply dock at $(50\text{ km}, 10\text{ km})$. What are the vessel's total distance traveled and the magnitude of its net displacement from the buoy to the supply dock?

    • A) Total distance: 70 km; Magnitude of net displacement: 50 km
    • B) Total distance: 80 km; Magnitude of net displacement: 50 km
    • C) Total distance: 80 km; Magnitude of net displacement: 40 km
    • D) Total distance: 100 km; Magnitude of net displacement: 40 km
12. 12.

    During a robotics evaluation, students program an autonomous ground vehicle to complete four distinct test runs between two markers, X and Y, set across an open hall. Run 1: The vehicle travels along a straight line directly from X to Y without changing direction. Run 2: The vehicle travels along a straight line from X toward Y, overshoots marker Y, and reverses along the same line to stop at Y. Run 3: The vehicle zig-zags back and forth across the hall while steadily advancing from X to Y. Run 4: The vehicle starts at X, navigates a complete closed loop around the hall, and stops back at X. In which of the test runs is the magnitude of the vehicle's displacement equal to the total distance traveled?

    • A) Run 1 only
    • B) Run 1 and Run 2 only
    • C) Run 1 and Run 3 only
    • D) Run 2 and Run 4 only
13. 13.

    An oceanographic sensor is deployed from a research ship deck located at $+6\text{ m}$ along a vertical coordinate axis where sea level is defined as the origin ($y = 0\text{ m}$) and upward is positive. The sensor is lowered straight down through the water column to a depth of $-74\text{ m}$ and is then hoisted upward to a sampling depth of $-24\text{ m}$, where it comes to rest. What are the sensor's final position, its net displacement from the ship deck, and the total distance it traveled during the operation?

    • A) Final position: $-30\text{ m}$, Net displacement: $-24\text{ m}$, Total distance: $124\text{ m}$
    • B) Final position: $-24\text{ m}$, Net displacement: $-30\text{ m}$, Total distance: $130\text{ m}$
    • C) Final position: $-24\text{ m}$, Net displacement: $-24\text{ m}$, Total distance: $130\text{ m}$
    • D) Final position: $-24\text{ m}$, Net displacement: $-30\text{ m}$, Total distance: $30\text{ m}$
14. 14.

    An autonomous security rover monitors the perimeter of a rectangular research compound, starting from the southwest corner defined as the coordinate origin (0 m, 0 m). The rover travels 80 m due east along the southern perimeter, turns north to travel 60 m along the eastern perimeter, and then turns west along the northern perimeter to travel 35 m before stopping at an inspection post. What are the total distance traveled by the rover and the magnitude of its net displacement from the starting point to the inspection post?

    • A) Total distance = 175 m; magnitude of displacement = 175 m
    • B) Total distance = 140 m; magnitude of displacement = 100 m
    • C) Total distance = 175 m; magnitude of displacement = 105 m
    • D) Total distance = 175 m; magnitude of displacement = 75 m
15. 15.

    A maintenance cart on a circular testing track with a radius of 30 m begins at a calibration post and travels along the curved rail to a service station located diametrically opposite its starting point. Engineers analyze the cart's telemetry to evaluate its motion along the perimeter versus its net change in position. What are the total distance traveled by the cart and the magnitude of its displacement for this journey?

    • A) Distance: 60 m; Magnitude of displacement: $30\pi$ m
    • B) Distance: $60\pi$ m; Magnitude of displacement: 60 m
    • C) Distance: $30\pi$ m; Magnitude of displacement: 0 m
    • D) Distance: $30\pi$ m; Magnitude of displacement: 60 m
16. 16.

    Two researchers, Sarah and Liam, evaluate the motion of an automated robotic rover moving along a straight line in a test facility. Sarah sets her coordinate origin at the facility entrance, while Liam sets his coordinate origin at a calibration pillar located 15 m further along the track in the positive direction. During the test, the rover starts from rest, travels forward, and then reverses to a final stop. Which statement correctly compares the values recorded or calculated by Sarah and Liam for the rover's initial position, total distance traveled, and displacement?

    • A) They record different initial positions, but determine identical values for both the total distance traveled and the displacement.
    • B) They determine identical values for the initial position and displacement, but calculate different values for the total distance traveled.
    • C) They record different initial positions and displacements, but calculate identical values for the total distance traveled.
    • D) They record different values for all three quantities: initial position, total distance traveled, and displacement.
17. 17.

    A wildlife biology team tracks two wolves along a straight east-west corridor, with positions measured in meters along an x-axis where east is positive and an observation tower marks the origin (x = 0). Wolf 1 begins at x = -40 m and walks directly east to a watering site at x = +20 m. Wolf 2 begins at x = +10 m, walks east to x = +90 m, and then turns back west to settle at a den at x = +70 m. Which statement correctly compares the displacements and total distances traveled by the two wolves?

    • A) Both wolves have the same displacement of +60 m, but Wolf 2 traveled a greater total distance than Wolf 1.
    • B) Wolf 2 has a greater displacement and a greater total distance than Wolf 1 because its final position is farther east.
    • C) Wolf 1 has a greater displacement than Wolf 2 because it crossed the origin, but both wolves traveled the same total distance.
    • D) Both wolves traveled the same total distance of 100 m, but Wolf 1 achieved a greater displacement because it moved without backtracking.
18. 18.

    During a field navigation exercise, two trainees start from the same base camp and travel to an observation post located 120 m due east. Trainee 1 walks in a straight line directly to the post, while Trainee 2 walks 90 m due north to a checkpoint before walking along a straight line directly to the observation post. Which statement correctly compares the total distance traveled and the displacement of the two trainees?

    • A) Both trainees have the same displacement of 120 m due east, but Trainee 2 travels a total distance of 240 m while Trainee 1 travels 120 m.
    • B) Trainee 2 has a greater displacement than Trainee 1 because Trainee 2 covers a total distance of 240 m compared to 120 m for Trainee 1.
    • C) Both trainees travel the same total distance of 240 m, but Trainee 1 has a displacement of 120 m while Trainee 2 has a displacement of 150 m.
    • D) Trainee 1 has a displacement of 120 m due east, whereas Trainee 2 has a displacement of 240 m directed toward the northeast.
19. 19.

    An autonomous agricultural robot starts at a charging hub, which serves as the reference origin. The robot travels 60 m due north along a crop row, turns to travel 80 m due east, and finally turns to travel 60 m due south before stopping. What are the robot's final position relative to the hub, the total distance traveled, and the magnitude of its displacement?

    • A) Final position: 80 m East; Distance: 200 m; Displacement magnitude: 80 m
    • B) Final position: 80 m East; Distance: 80 m; Displacement magnitude: 200 m
    • C) Final position: At the hub; Distance: 200 m; Displacement magnitude: 0 m
    • D) Final position: 100 m Northeast; Distance: 140 m; Displacement magnitude: 100 m
20. 20.

    An automated cart in a fulfillment center travels along a straight track calibrated in meters, where the positive direction points east. Starting at an initial position of $+12\text{ m}$, the cart drives east to a restocking station at $+28\text{ m}$ and then travels west in a straight line to an unloading dock at $-8\text{ m}$. What are the total distance traveled and the displacement of the cart for this complete journey?

    • A) Distance: 20 m; Displacement: +20 m
    • B) Distance: 36 m; Displacement: -8 m
    • C) Distance: 52 m; Displacement: -20 m
    • D) Distance: 52 m; Displacement: +20 m