Speed and velocity Transitional Reasoning Practice

Questions

1. 1.

   A robotic crawler inspects a straight drainage pipe calibrated along a coordinate axis where the positive direction points toward the pipe outlet. The crawler starts at position $x = +15\text{ m}$ and concludes its run at position $x = -25\text{ m}$ after an elapsed time of 20 s. Due to back-and-forth scanning of pipe seams, the crawler's odometer records a total distance of 60 m during this run. What are the crawler's average velocity and average speed over the 20 s interval?

   • A) Average velocity = +2.0 m/s; Average speed = 3.0 m/s
   • B) Average velocity = -3.0 m/s; Average speed = 3.0 m/s
   • C) Average velocity = -2.0 m/s; Average speed = 3.0 m/s
   • D) Average velocity = -2.0 m/s; Average speed = 2.0 m/s
2. 2.

   Two automated test shuttles, Shuttle P and Shuttle Q, travel along a straight 1200 m guideway between two stations using the same two operational speeds: 10 m/s and 30 m/s. Shuttle P travels the first 600 m at 10 m/s and the remaining 600 m at 30 m/s, whereas Shuttle Q operates at 10 m/s for the first half of its total travel time and at 30 m/s for the second half of its total travel time. Based on the definition of average speed, which statement correctly compares the overall average speeds of the two shuttles?

   • A) Shuttle Q has a higher average speed (20 m/s) than Shuttle P (15 m/s) because Shuttle P spends more time traveling at the slower speed.
   • B) Both shuttles achieve the same average speed (20 m/s) because both vehicles divide their motion equally between 10 m/s and 30 m/s.
   • C) Shuttle P has a higher average speed (20 m/s) than Shuttle Q (15 m/s) because covering equal distances at each speed maximizes overall efficiency.
   • D) Shuttle Q has a higher average speed (25 m/s) than Shuttle P (20 m/s) because average speed over time is weighted toward the maximum instantaneous speed.
3. 3.

   An automated transit pod travels along a straight 600 m guideway between two passenger terminals. The pod covers the first 240 m of the guideway at a constant speed of 20 m/s. To achieve a scheduled average speed of 30 m/s over the entire 600 m journey, at what constant speed must the pod travel across the remaining 360 m?

   • A) 40 m/s
   • B) 45 m/s
   • C) 50 m/s
   • D) 36 m/s
4. 4.

   An engineering team tests two automated carts that each complete a closed trip returning to their exact starting points over a 30 s interval, resulting in an average velocity of zero for both carts. Cart 1 moves back and forth along a single straight track, while Cart 2 travels at a steady rate around a closed circular track. Which statement correctly evaluates the instantaneous speeds of the two carts during these test runs?

   • A) Both carts must reach an instantaneous speed of zero at some point because an average velocity of zero requires an object to come to rest.
   • B) Cart 1 must have an instantaneous speed of zero at its turnaround point, whereas Cart 2 can complete its trip without its instantaneous speed ever dropping to zero.
   • C) Cart 2 must have an instantaneous speed of zero when changing direction around the bend, whereas Cart 1 can maintain a constant speed throughout its reversal.
   • D) Neither cart is required to reach an instantaneous speed of zero as long as the total distance traveled divided by the elapsed time is greater than zero.
5. 5.

   An automated highway enforcement system uses two camera gantries positioned along a straight, unidirectional 30 km stretch of highway with a posted speed limit of 80 km/h. A vehicle passes the first gantry at a recorded instantaneous speed of 70 km/h and passes the second gantry exactly 20 minutes later at an instantaneous speed of 70 km/h. Based on the relationship between instantaneous speed and average speed, which conclusion regarding the vehicle's motion is correct?

   • A) The driver complied with the speed limit because the average of the two recorded instantaneous speeds was only 70 km/h.
   • B) The driver complied with the speed limit because an object's instantaneous speed cannot exceed the posted threshold if both endpoint readings are compliant.
   • C) The driver violated the speed limit because their average speed was 90 km/h, proving that their instantaneous speed reached at least 90 km/h at some point during the trip.
   • D) The driver violated the speed limit because an average speed of 60 km/h along a straight highway requires doubling the instantaneous speed mid-route.
6. 6.

   An aerial inspection drone operates along a straight corridor aligned with an axis where the positive direction points from a base station toward a remote tower. The drone flies away from the base station toward the tower, immediately reverses direction, and flies straight back toward the base station before landing at an intermediate pad after a total flight time of 50 s. Telemetry data record an average speed of 14 m/s and an average velocity of +6.0 m/s over the entire 50 s flight. Based on these logged data, what total distance did the drone travel on its return flight?

   • A) 200 m
   • B) 500 m
   • C) 350 m
   • D) 300 m
7. 7.

   An agricultural robotics team evaluates two autonomous rovers, Alpha and Beta, operating over an identical duration of 40 s across a flat field. Rover Alpha follows a meandering route, covering a total distance of 160 m to end at a net displacement of 40 m from its starting point. Rover Beta moves along a straight, unidirectional path, covering a total distance of 80 m to end at a net displacement of 80 m from its starting point. Based on these logged test data, which statement correctly compares the average speeds and the magnitudes of the average velocities of the two rovers?

   • A) Rover Alpha has both a greater average speed and a greater magnitude of average velocity than Rover Beta.
   • B) Rover Alpha has a greater average speed than Rover Beta, but Rover Beta has a greater magnitude of average velocity than Rover Alpha.
   • C) Rover Beta has both a greater average speed and a greater magnitude of average velocity than Rover Alpha.
   • D) Rover Alpha and Rover Beta have identical magnitudes of average velocity because the testing time is the same, but Rover Alpha has a greater average speed.
8. 8.

   A logistics telemetry console monitors two automated rail carts, Cart X and Cart Y, moving along a straight single-track corridor aligned with a coordinate axis where the positive direction points towards a central warehouse. At a recorded instant, the console registers a velocity of -16 m/s for Cart X and a velocity of +10 m/s for Cart Y. Based on these velocity readings, which statement correctly compares the speeds of the two carts and identifies their directions of motion relative to the central warehouse?

   • A) Cart Y moves faster than Cart X because its velocity has a positive value, and both carts travel toward the central warehouse.
   • B) Cart Y moves faster than Cart X because +10 m/s is algebraically greater than -16 m/s, and Cart X travels toward the central warehouse while Cart Y travels away from it.
   • C) Cart X moves faster than Cart Y because its speed is 16 m/s compared to Cart Y's 10 m/s, but both carts travel in the same direction toward the central warehouse.
   • D) Cart X moves faster than Cart Y because its speed is 16 m/s compared to Cart Y's 10 m/s, and Cart X travels away from the central warehouse while Cart Y travels toward it.
9. 9.

   During a field trial along a curved scenic highway, an autonomous test vehicle logs its motion between two waypoints using two navigation devices. Device X integrates instantaneous speedometer readings to determine the vehicle's average speed as 18 m/s, while Device Y calculates the magnitude of the average velocity as 12 m/s using the straight-line GPS displacement between the waypoints and the total trip duration. Which statement correctly explains why the value reported by Device X is greater than the value reported by Device Y?

   • A) Device X accounts for the vehicle's instantaneous accelerations around curves, whereas Device Y assumes the vehicle moved with zero net acceleration.
   • B) Device X calculates total distance divided by elapsed time, whereas Device Y calculates the smaller straight-line displacement divided by the same elapsed time.
   • C) Device X records instantaneous velocity at the sharpest curve, whereas Device Y averages the initial and final instantaneous velocities.
   • D) Device X measures a vector quantity that compounds over directional changes, whereas Device Y measures a scalar quantity that ignores direction.
10. 10.

    A telemetry analysis system validates the motion logs of experimental ground vehicles operating across a flat testing facility over a 60 s interval. Due to sensor errors, some recorded logs contain kinematic contradictions. Based on the fundamental definitions of speed and velocity, which of the following reported vehicle records is physically possible?

    • A) A rover records an average speed of 2.5 m/s and an average velocity magnitude of 4.0 m/s over the interval.
    • B) A transport cart records an average speed of 3.0 m/s, an average velocity magnitude of 1.8 m/s, and an instantaneous speed of 0 m/s at the 20 s mark.
    • C) A patrol bot records an average speed of 0 m/s over the interval while logging an instantaneous velocity of 2.0 m/s due north at the 15 s mark.
    • D) A utility vehicle records a constant velocity of 5.0 m/s due east throughout the entire interval, but its average speed over the interval is logged as 3.5 m/s.
11. 11.

    A research team evaluates the navigation log of an autonomous inspection drone operating across a flat testing ground. During a continuous 40 s trial, the drone maintains a constant instantaneous speed of 8.0 m/s at every moment. The navigation log reports that the magnitude of the drone's average velocity over this entire 40 s interval is also exactly 8.0 m/s. Based on kinematic principles, which conclusion regarding the drone's motion during this trial must be true?

    • A) The drone moved along a straight line in a single, unchanging direction throughout the trial.
    • B) The drone completed a closed circular loop and returned to its starting point at the end of the trial.
    • C) The drone moved along a curved path with a constant radius of curvature throughout the trial.
    • D) The drone moved along a straight line but reversed its direction of motion midway through the trial.
12. 12.

    An automated rover navigates a curved test path across a laboratory floor. At a specific timestamp, its instantaneous velocity vector has a magnitude of 0.60 m/s directed at 30° north of east. Over the entire 20 s trial, the rover covers a total path length of 15 m and finishes with a net straight-line displacement of 9.0 m from its starting point. Based on these kinematic data, which statement correctly identifies the rover's instantaneous speed at that timestamp and compares its average speed with the magnitude of its average velocity over the full trial?

    • A) The instantaneous speed is greater than 0.60 m/s, and the average speed (0.75 m/s) is equal to the magnitude of the average velocity (0.75 m/s).
    • B) The instantaneous speed is equal to 0.60 m/s, and the average speed (0.75 m/s) is greater than the magnitude of the average velocity (0.45 m/s).
    • C) The instantaneous speed is equal to 0.60 m/s, and the average speed (0.45 m/s) is less than the magnitude of the average velocity (0.75 m/s).
    • D) The instantaneous speed is less than 0.60 m/s, and the average speed (0.45 m/s) is equal to the magnitude of the average velocity (0.45 m/s).
13. 13.

    During an efficiency trial on a straight, unidirectional test track, an electric test car travels at a constant speed of 12 m/s for 20 s, and then continues along the same straight path at a constant speed of 24 m/s for the subsequent 30 s. Based on these telemetry records, what is the car's average speed over the entire 50 s trial?

    • A) 16.0 m/s
    • B) 16.8 m/s
    • C) 18.0 m/s
    • D) 19.2 m/s
14. 14.

    A logistics robot navigates along a straight warehouse aisle calibrated along a coordinate axis. Starting from an initial position of 0 m, the robot moves forward to +60 m at a constant velocity of +4.0 m/s, stops for 5.0 s to scan a misplaced package, and then travels to +50 m at a constant velocity of -2.0 m/s. Based on this logged operational sequence, what is the robot's average velocity over the entire duration of the motion?

    • A) +2.0 m/s
    • B) +2.8 m/s
    • C) +2.5 m/s
    • D) +1.0 m/s
15. 15.

    A passenger train travels along a straight, level railway connecting two suburban stations separated by a total distance of 12 km. The train travels the first 6.0 km of the route at a steady speed of 20 m/s and covers the remaining 6.0 km at a steady speed of 30 m/s without stopping. Based on these recorded operating data, what is the train's average speed over the entire 12 km journey?

    • A) 20 m/s
    • B) 22 m/s
    • C) 24 m/s
    • D) 25 m/s
16. 16.

    Two autonomous delivery pods, Pod X and Pod Y, depart from a central distribution center at the exact same moment and arrive at a remote outpost simultaneously. Pod X travels along a winding suburban detour covering a total path length of 18 km, while Pod Y travels along a direct straight-line expressway covering a distance of 12 km. Based on these trip records, which statement correctly compares the average speeds and the magnitudes of the average velocities of the two pods over the entire journey?

    • A) Pod X has a greater average speed and a greater magnitude of average velocity than Pod Y.
    • B) Both pods have the same average speed and the same magnitude of average velocity.
    • C) Pod X has a greater average speed than Pod Y, but both pods have the same magnitude of average velocity.
    • D) Pod Y has a greater magnitude of average velocity than Pod X, but both pods have the same average speed.
17. 17.

    A telemetry system monitors an automated car across three test sections: in Section 1, it accelerates from 20 km/h to 50 km/h along a straight lane; in Section 2, it rounds a curved bend at a steady 50 km/h; and in Section 3, it maintains 50 km/h along a straight stretch. During which of these sections is the car's velocity changing?

    • A) Section 1 only
    • B) Sections 1 and 2 only
    • C) Sections 2 and 3 only
    • D) Sections 1, 2, and 3
18. 18.

    During a safety trial, an autonomous cart travels around a closed circular track of radius 50 m at a constant speedometer reading of 5.0 m/s, returning to its exact starting point after completing one full lap. A technician evaluates the motion data recorded by the onboard navigation system over this single lap. Which statement accurately describes the cart's speed and velocity during this trial?

    • A) Because the speedometer reading is constant, the cart's instantaneous velocity remains constant throughout the entire lap.
    • B) The cart's average speed is 0 m/s because the cart returns to its original starting position.
    • C) The magnitude of the cart's average velocity equals 5.0 m/s because its rate of travel along the path does not vary.
    • D) The cart's instantaneous velocity continuously changes despite having a constant speed, and its average velocity over the complete lap is zero.
19. 19.

    A courier drone delivers emergency medicine by flying 300 m due north in 30 s, and then immediately turns to fly 400 m due east in 20 s to reach a field clinic. Assuming flight in a single horizontal plane, what are the drone's average speed and the magnitude of its average velocity over the entire 50 s trip?

    • A) Average speed is 10 m/s, and the magnitude of average velocity is 14 m/s.
    • B) Average speed is 14 m/s, and the magnitude of average velocity is 14 m/s.
    • C) Average speed is 15 m/s, and the magnitude of average velocity is 10 m/s.
    • D) Average speed is 14 m/s, and the magnitude of average velocity is 10 m/s.
20. 20.

    An automated inspection rover travels along a straight pipe segment, moving 120 m due east in 30 s before turning around to travel 40 m due west along the exact same path in 10 s. What are the rover's average speed and the magnitude of its average velocity over the entire 40 s interval?

    • A) Average speed is 2.0 m/s, and average velocity magnitude is 4.0 m/s.
    • B) Average speed is 4.0 m/s, and average velocity magnitude is 2.0 m/s.
    • C) Average speed is 4.0 m/s, and average velocity magnitude is 4.0 m/s.
    • D) Average speed is 2.0 m/s, and average velocity magnitude is 2.0 m/s.

Answers and step-by-step solutions appear after you finish the test.