Speed and velocity Transitional Reasoning Download PDF

Questions

1. 1.

   An environmental research team launches three autonomous surface vessels—Vessel 1, Vessel 2, and Vessel 3—from a research dock toward a sensor buoy anchored 600 m due east. All three vessels depart at $t = 0\text{ s}$ and arrive at the buoy at $t = 120\text{ s}$: Vessel 1 travels directly along the straight 600 m path at a constant speed; Vessel 2 follows an 840 m curved detour around a reef; and Vessel 3 travels 360 m east along the straight path, pauses for 30 s to record water temperature, and then completes the remaining 240 m east. Based on the physical definitions of speed and velocity, which statement correctly compares the motion of the three vessels over this 120-second trial?

   • A) Vessel 1 has a greater average velocity than Vessel 3 because Vessel 3 was stationary for 30 s, while Vessel 2 has the greatest average velocity because it covered the longest path.
   • B) Vessel 1 and Vessel 3 have different average speeds because Vessel 3 stopped during transit, but all three vessels have different average velocities due to their different travel profiles.
   • C) All three vessels have identical average velocities of $5.0\text{ m/s}$ due east, while Vessel 2 has a greater average speed ($7.0\text{ m/s}$) than Vessels 1 and 3, which share an equal average speed of $5.0\text{ m/s}$.
   • D) Because all three vessels depart together and reach the buoy simultaneously, both their average speeds and their average velocities are strictly equal across all three vessels.
2. 2.

   An automated surveillance drone flies across a flat test range along two consecutive straight segments. It first travels 600 m due south at a constant speed of 20 m/s, and immediately turns to travel 800 m due west at a constant speed of 40 m/s. What are the drone's average speed and the magnitude of its average velocity over the entire flight?

   • A) Average speed is 30 m/s, and the magnitude of average velocity is 25 m/s.
   • B) Average speed is 30 m/s, and the magnitude of average velocity is 20 m/s.
   • C) Average speed is 28 m/s, and the magnitude of average velocity is 28 m/s.
   • D) Average speed is 28 m/s, and the magnitude of average velocity is 20 m/s.
3. 3.

   A logistics team evaluates two automated guided carts navigating across a flat factory floor between a dispatch bay and an assembly station located 150 m due north. Cart 1 follows a direct straight-line route of 150 m in 30 s, whereas Cart 2 takes a detour around storage racks to cover a total path length of 250 m in 50 s. Based on the physical definitions of speed and velocity, which statement correctly compares the motion of the two carts over their respective journeys?

   • A) Both carts have the same average velocity of 3.0 m/s due north because their starting and ending points are identical, but Cart 2 has a higher average speed.
   • B) Cart 2 has a greater average speed than Cart 1 because it covers 250 m instead of 150 m, while both carts share the same average velocity magnitude of 5.0 m/s.
   • C) Cart 1 has both a greater average speed and a greater average velocity magnitude than Cart 2 because it completes its journey in a shorter total time.
   • D) Both carts have the same average speed of 5.0 m/s, but Cart 1 has a greater average velocity magnitude (5.0 m/s) than Cart 2 (3.0 m/s).
4. 4.

   An engineering team evaluates four autonomous rovers (P, Q, R, and S) operating on a flat test course over a 30-second trial. Rover P travels along a straight line for 12 s, pauses for 6 s, and resumes moving in the same direction along that line for 12 s; Rover Q follows a circular curved path at a constant speed; Rover R travels along a straight path for 20 s and immediately reverses direction along the same path for 10 s; and Rover S travels 40 m due north followed by 30 m due east. Based on the physical definitions of speed and velocity, for which rover is the magnitude of the average velocity strictly equal to the average speed over the entire 30-second trial?

   • A) Rover Q, because it is the only rover that maintains a constant instantaneous speed throughout the entire trial.
   • B) Rover P, because its motion occurs entirely along a straight line in a single unchanging direction, making its displacement magnitude equal to the total distance traveled.
   • C) Rover R, because its forward and backward segments occur along the same straight line, preserving a constant ratio between position and time.
   • D) Rover S, because both of its straight segments are executed at constant velocities that sum directly to its total displacement.
5. 5.

   A sports scientist records the motion of a sprinter competing in a 100 m straight dash along the positive x-axis. The sprinter starts from rest at 0 m/s, reaches a peak instantaneous speed of 12.0 m/s at the 60 m mark, and crosses the finish line at 10.0 s with an instantaneous velocity of +11.0 m/s. An analyst asserts that the sprinter's average velocity must be +5.5 m/s based on the arithmetic mean of the initial and final velocities. Based on the physical definitions of motion, what is the sprinter's actual average velocity, and how should the analyst's assertion be evaluated?

   • A) The average velocity is +10.0 m/s; the arithmetic mean formula applies only to motion with constant acceleration, whereas average velocity is fundamentally defined as total displacement divided by elapsed time.
   • B) The average velocity is +10.0 m/s; the arithmetic mean formula is invalid because the peak instantaneous speed was 12.0 m/s, meaning the average velocity must be calculated by averaging the peak and final velocities.
   • C) The average velocity is +5.5 m/s; the analyst's assertion is correct because in any straight-line motion, average velocity is defined as the midpoint between the initial and final instantaneous velocities.
   • D) The average velocity is +11.0 m/s; because the sprinter maintained forward motion throughout the dash, the average velocity is determined solely by the final instantaneous velocity upon crossing the finish line.
6. 6.

   An engineer analyzes the telemetry data of an automated cart moving along a straight one-dimensional track aligned with the x-axis. Over the interval from $t = 0\text{ s}$ to $t = 10\text{ s}$, the cart's average velocity is $+2.0\text{ m/s}$, but at the specific moment $t = 5.0\text{ s}$, its instantaneous velocity is recorded as $-3.0\text{ m/s}$. Based on the physical definitions of speed and velocity, which deduction about the cart's motion must be correct?

   • A) The cart moved exclusively in the positive direction throughout the entire 10-second interval because its net average velocity is positive.
   • B) The cart's instantaneous speed at $t = 5.0\text{ s}$ is $-3.0\text{ m/s}$, demonstrating that speed inherits a negative sign whenever velocity is directed along the negative coordinate axis.
   • C) The cart's average speed over the 10-second interval must be exactly equal to $2.0\text{ m/s}$ because the motion is entirely restricted to a one-dimensional straight track.
   • D) The cart must have reversed its direction of motion during the interval, ensuring that its average speed over the 10 seconds is strictly greater than $2.0\text{ m/s}$.
7. 7.

   In a physics laboratory, a cart equipped with a 2.0 cm wide flag rolls down a straight, inclined track through two photogates positioned 1.20 m apart. The cart's flag interrupts Gate 1 for 0.050 s, takes 2.00 s to travel from Gate 1 to Gate 2, and interrupts Gate 2 for 0.025 s. Based on the physical definitions of motion, what are the cart's average speed between the two photogates and its instantaneous speed as it passes Gate 2?

   • A) Average speed = 0.60 m/s; Instantaneous speed at Gate 2 = 0.80 m/s
   • B) Average speed = 0.80 m/s; Instantaneous speed at Gate 2 = 0.60 m/s
   • C) Average speed = 0.60 m/s; Instantaneous speed at Gate 2 = 0.40 m/s
   • D) Average speed = 0.40 m/s; Instantaneous speed at Gate 2 = 0.80 m/s
8. 8.

   A traffic safety team reviews automated monitoring data along a curved section of highway connecting two interchanges where the posted speed limit is 80 km/h. The road distance along the winding highway between two camera checkpoints is 6.0 km, whereas the direct straight-line distance between them is 4.8 km. A vehicle is recorded passing the first checkpoint at 08:00 and the second checkpoint at 08:04. Based on the physical definitions of speed and velocity, which evaluation correctly identifies whether the vehicle violated the speed limit and states the values of its average speed and the magnitude of its average velocity?

   • A) The car did not violate the speed limit; its average speed was 72 km/h, and the magnitude of its average velocity was 90 km/h.
   • B) The car did not violate the speed limit; its average speed was 90 km/h, and the magnitude of its average velocity was 72 km/h.
   • C) The car violated the speed limit; its average speed was 72 km/h, and the magnitude of its average velocity was 90 km/h.
   • D) The car violated the speed limit; its average speed was 90 km/h, and the magnitude of its average velocity was 72 km/h.
9. 9.

   A field station monitors an autonomous planetary rover navigating across a flat testing arena mapped onto a two-dimensional Cartesian coordinate grid. At time t = 0 s, the rover is located at coordinates (15 m, 20 m), and at t = 25 s, its telemetry beacon records its position at (75 m, 100 m). During this 25-second interval, the rover's wheel odometer measures a total distance traveled of 175 m along its curved path. What are the rover's average speed and the magnitude of its average velocity over the entire 25 s test?

   • A) Average speed = 4.0 m/s; Average velocity magnitude = 7.0 m/s
   • B) Average speed = 7.0 m/s; Average velocity magnitude = 5.6 m/s
   • C) Average speed = 7.0 m/s; Average velocity magnitude = 4.0 m/s
   • D) Average speed = 7.0 m/s; Average velocity magnitude = 5.0 m/s
10. 10.

    An autonomous agricultural rover collects soil data across a level field by following a programmed survey route. The rover travels 180 m due east in 40 s, turns and travels 240 m due north in 60 s, and then travels 180 m due west in 20 s to reach its final sensor waypoint. Over this entire 120 s journey, what are the rover's average speed and average velocity?

    • A) Average speed is 2.0 m/s, and average velocity is 5.0 m/s due north.
    • B) Average speed is 5.0 m/s, and average velocity is 5.0 m/s due north.
    • C) Average speed is 3.5 m/s, and average velocity is 2.0 m/s due east.
    • D) Average speed is 5.0 m/s, and average velocity is 2.0 m/s due north.
11. 11.

    A robotics technician evaluates the motion of an automated inspection cart along a 120 m straight test track under two different speed programs. In Mode 1, the cart travels at 10 m/s for the first half of its total travel time and 30 m/s for the second half of its total travel time. In Mode 2, the cart travels at 10 m/s for the first 60 m of the track and 30 m/s for the remaining 60 m. What are the average speeds of the cart in Mode 1 and Mode 2, respectively?

    • A) Mode 1: 20 m/s; Mode 2: 15 m/s
    • B) Mode 1: 20 m/s; Mode 2: 20 m/s
    • C) Mode 1: 15 m/s; Mode 2: 20 m/s
    • D) Mode 1: 15 m/s; Mode 2: 15 m/s
12. 12.

    During a field trial on a flat lawn, an autonomous robotic mower navigates an S-shaped curved path from its charging station to a maintenance dock in 50 s. The mower's wheel odometer records a total path length of 120 m, while GPS confirms that the dock is located 40 m due north of the charging station. Which statement correctly compares the mower's instantaneous kinematic quantities and determines its average speed and average velocity for the entire trial?

    • A) At each instant, the mower's instantaneous speed is greater than the magnitude of its instantaneous velocity, resulting in an average speed of 2.4 m/s and an average velocity of 2.4 m/s due north.
    • B) At each instant, the mower's instantaneous speed equals the magnitude of its instantaneous velocity, resulting in an average speed of 0.80 m/s and an average velocity of 2.4 m/s due north.
    • C) At each instant, the mower's instantaneous speed equals the magnitude of its instantaneous velocity, resulting in an average speed of 2.4 m/s and an average velocity of 0.80 m/s due north.
    • D) At each instant, the mower's instantaneous speed is less than the magnitude of its instantaneous velocity, resulting in an average speed of 0.80 m/s and an average velocity of 0.80 m/s due north.
13. 13.

    A marine survey vessel departs from an offshore platform and follows an irregular, winding course across the ocean while mapping the seabed. At the end of a 4.0-hour survey, the vessel's satellite navigation system indicates that its final position is located 24 km due east of the platform, even though its engine log registers a total distance traveled of 72 km. Based on the physical definitions of displacement, speed, and velocity, which statement correctly identifies the vessel's average velocity and provides the correct physical justification for its direction?

    • A) 6.0 km/h due east, because average velocity is the net displacement divided by elapsed time and points in the direction of displacement regardless of the path taken.
    • B) 18 km/h due east, because average velocity is the total distance traveled divided by elapsed time directed toward the final position.
    • C) 6.0 km/h with an undefined direction, because average velocity cannot have a specific direction when a craft continuously changes headings along a curved path.
    • D) 18 km/h in the direction of the vessel's final heading, because the direction of average velocity is determined by the vessel's orientation when the survey ends.
14. 14.

    A robotics engineer audits the performance logs of four autonomous test vehicles operating over an identical 10-second interval across a testing arena. The log records report the following pairs of average speed and average velocity magnitude: Vehicle W (4.0 m/s and 2.5 m/s), Vehicle X (3.0 m/s and 3.0 m/s), Vehicle Y (2.0 m/s and 3.5 m/s), and Vehicle Z (5.0 m/s and 0.0 m/s). Based on the physical definitions of distance, displacement, speed, and velocity, which vehicle's log indicates an impossible motion that confirms a sensor error?

    • A) Vehicle W, because the magnitude of its average velocity is strictly less than its average speed.
    • B) Vehicle X, because an object's average speed cannot be equal to the magnitude of its average velocity.
    • C) Vehicle Y, because the magnitude of average velocity cannot exceed the average speed over any time interval.
    • D) Vehicle Z, because an object cannot have an average velocity magnitude of zero while maintaining a non-zero average speed.
15. 15.

    An autonomous inspection drone travels along a straight, unidirectional test corridor from Station A to Station B, which are 480 m apart. It covers the first 240 m at a constant velocity of 12 m/s toward Station B. To achieve an overall average velocity of 16 m/s toward Station B for the entire 480 m trip, what constant velocity must the drone maintain across the remaining 240 m?

    • A) 20 m/s toward Station B
    • B) 24 m/s toward Station B
    • C) 18 m/s toward Station B
    • D) 28 m/s toward Station B
16. 16.

    An engineering team evaluates the telemetry data of an automated guided cart operating in a warehouse. Over a 30-second interval, the cart's digital speedometer maintains a constant reading of 1.5 m/s while the cart travels along an aisle, executes a 90-degree left turn, and continues along a cross aisle. A technician asserts that because the cart's speedometer reading never varied from 1.5 m/s, its velocity remained constant throughout the entire interval. Based on the physical definitions of speed and velocity, which evaluation of the technician's assertion is correct?

    • A) The assertion is correct because velocity is defined solely by the time rate at which distance is traversed along any chosen path.
    • B) The assertion is incorrect because velocity is a vector quantity that includes direction, so changing heading alters velocity even at constant speed.
    • C) The assertion is correct because the magnitude of instantaneous velocity matched the 1.5 m/s speedometer reading at every instant.
    • D) The assertion is incorrect because changing direction along perpendicular aisles reduces the cart's average speed over the interval to zero.
17. 17.

    Two autonomous exploration rovers, Alpha and Beta, travel from a base station to a remote sensor site across flat terrain in the same elapsed time of 40 s. Rover Alpha follows a direct, straight-line path of 160 m, while Rover Beta navigates around an obstacle along a curved path measuring 240 m. Which statement correctly compares the average speed and average velocity of the two rovers during this transit?

    • A) Both rovers have the same average speed, but Rover Alpha has a greater average velocity because it moved along a direct path.
    • B) Both rovers have the same average velocity, but Rover Beta has a greater average speed because it traveled a greater distance in the same time.
    • C) Rover Beta has both a greater average speed and a greater magnitude of average velocity because it traversed a longer overall trajectory.
    • D) Rover Alpha has both a greater average speed and a greater magnitude of average velocity because a straight path yields the most efficient displacement.
18. 18.

    An automated delivery drone travels directly along a straight path from docking station X to station Y, covering a distance of 600 m at a constant speed of 15 m/s. Upon reaching station Y, the drone immediately returns to station X along the same straight path at a constant speed of 10 m/s. What are the drone's average speed and average velocity for the entire round trip from station X back to station X?

    • A) Average speed is 12.5 m/s, and average velocity is 12.5 m/s.
    • B) Average speed is 12.5 m/s, and average velocity is 0 m/s.
    • C) Average speed is 12 m/s, and average velocity is 12 m/s toward station X.
    • D) Average speed is 12 m/s, and average velocity is 0 m/s.
19. 19.

    A research rover navigates around a curved hazard during a field test, traveling along a semicircular path of length 157 m in 20.0 s. The direct straight-line distance between the rover's starting point and ending point across the hazard is 100 m. What are the rover's average speed and the magnitude of its average velocity during this test?

    • A) Average speed is 5.00 m/s, and average velocity magnitude is 7.85 m/s.
    • B) Average speed is 7.85 m/s, and average velocity magnitude is 5.00 m/s.
    • C) Average speed is 7.85 m/s, and average velocity magnitude is 7.85 m/s.
    • D) Average speed is 5.00 m/s, and average velocity magnitude is 0 m/s.
20. 20.

    An automated delivery vehicle moves along a straight east-west aisle in a warehouse. It travels 120 m east in 20 s, stops for 10 s to scan an item, and then travels 60 m west in 30 s. What are the vehicle's average speed and the magnitude of its average velocity for the entire 60 s interval?

    • A) Average speed is 2.0 m/s, and average velocity magnitude is 2.0 m/s.
    • B) Average speed is 3.0 m/s, and average velocity magnitude is 1.0 m/s.
    • C) Average speed is 1.0 m/s, and average velocity magnitude is 3.0 m/s.
    • D) Average speed is 3.6 m/s, and average velocity magnitude is 1.2 m/s.