Constant velocity motion Transitional Reasoning Download PDF

Questions

1. 1.

   An autonomous mobile robot travels along a straight corridor marked with a position coordinate axis, maintaining a constant velocity throughout its run. A telemetry unit records its motion, generating a linear position-time graph with a position intercept at $x = -15\text{ m}$ at time $t = 0\text{ s}$ and a time intercept at $t = 6.0\text{ s}$ where $x = 0\text{ m}$. At what time $t$ from the start of the recording will the robot reach an inspection gateway located at $x = +45\text{ m}$?

   • A) 18.0 s
   • B) 24.0 s
   • C) 30.0 s
   • D) 12.0 s
2. 2.

   An automated freight train travels at a constant velocity of 20 m/s along a straight track that passes through a tunnel. The train remains completely inside the tunnel for a duration of 25 s. The total time elapsed from the instant the front of the train enters the tunnel until its rear end completely emerges from the opposite end is 35 s. What is the length of the train?

   • A) 50 m
   • B) 80 m
   • C) 200 m
   • D) 100 m
3. 3.

   An autonomous delivery robot travels along a straight corridor from Hub A to Hub B at a constant velocity. A monitoring system records that at a certain moment, the ratio of the distance the robot has traveled from Hub A to the distance remaining to Hub B is 1:3. After the robot continues moving at the same constant velocity for an additional 12 minutes, the ratio of distance traveled to distance remaining becomes 3:1. How much total time does the robot require to complete the entire trip from Hub A to Hub B?

   • A) 18 minutes
   • B) 24 minutes
   • C) 32 minutes
   • D) 36 minutes
4. 4.

   An automated cart moves along a straight horizontal track in two sequential stages of constant velocity motion. In the first stage, the cart travels in the positive direction at a constant speed $v$ for a time interval $t$. In the second stage, it immediately changes direction and travels in the negative direction at a constant speed of $0.5v$ for a time interval of $3t$. What is the ratio of the total distance traveled by the cart to the magnitude of its net displacement over the entire motion?

   • A) 2.0
   • B) 3.0
   • C) 5.0
   • D) 8.0
5. 5.

   In an automated greenhouse, an irrigation boom travels along a straight 60 m overhead rail at a constant velocity, starting from the beginning of the rail at time $t = 0\text{ s}$. A position sensor records that the boom passes the 24 m mark at $t = 16\text{ s}$. Upon reaching the end of the 60 m rail, the boom pauses for 10 s to refill its water reservoir and then returns to the starting position at the same constant speed. What is the total time elapsed from $t = 0\text{ s}$ until the boom fully returns to the start of the rail?

   • A) 90 s
   • B) 80 s
   • C) 74 s
   • D) 50 s
6. 6.

   Two autonomous rovers, Rover 1 and Rover 2, travel in the same direction along parallel straight tracks, each maintaining a constant velocity. Rover 1 moves at a constant velocity of 6.0 m/s, while Rover 2 moves at a constant velocity of 10.0 m/s. At time $t = 8.0\text{ s}$, tracking data indicates that Rover 1 is 40 m ahead of Rover 2. Assuming both rovers continue their motion indefinitely, at what time $t$ will Rover 2 be 40 m ahead of Rover 1?

   • A) 16.0 s
   • B) 18.0 s
   • C) 20.0 s
   • D) 28.0 s
7. 7.

   A robotic cart travels at a constant speed along a straight, uniform moving walkway in an automated terminal. When moving in the same direction as the walkway, the cart travels a distance of 90 m relative to the ground in 18 s. When traveling in the opposite direction at the exact same speed relative to the walkway surface, it requires 45 s to travel the same 90 m distance relative to the ground. What is the constant speed of the moving walkway relative to the ground?

   • A) 3.5 m/s
   • B) 2.5 m/s
   • C) 2.0 m/s
   • D) 1.5 m/s
8. 8.

   A municipal transit corridor has two synchronized traffic signals positioned 420 m apart along a straight road. Signal 1 turns green at time t = 0 s, while Signal 2 turns green at t = 20 s and remains green for 15 s before switching to red. An electric shuttle passes Signal 1 at the exact moment it turns green and travels along the corridor at a constant velocity. What is the minimum constant velocity the shuttle can maintain to pass Signal 2 while it is still green?

   • A) 28 m/s
   • B) 21 m/s
   • C) 12 m/s
   • D) 14 m/s
9. 9.

   Along a straight 180 m transport track in a logistics facility, an intermediate inspection station is located at an unknown distance from the starting line. Cart 1 departs from the starting line at time $t = 0\text{ s}$ and travels toward the finish line at a constant velocity of 6.0 m/s. Cart 2 departs from the inspection station at time $t = 5.0\text{ s}$ and travels in the same direction toward the finish line at a constant velocity of 4.0 m/s. If both carts reach the finish line at the exact same instant, what is the distance from the starting line to the inspection station?

   • A) 60 m
   • B) 80 m
   • C) 100 m
   • D) 120 m
10. 10.

    A guided laboratory cart travels along a straight track between two fixed markers at a constant velocity. At its baseline speed, the cart takes 8.0 s to cover the distance between the markers. When its velocity is increased by 2.0 m/s, it covers the same distance in 6.0 s while maintaining that new velocity steadily. What is the distance between the two markers?

    • A) 24 m
    • B) 36 m
    • C) 48 m
    • D) 64 m
11. 11.

    On two straight, parallel tracks in an automated logistics center, Cargo Pod A and Cargo Pod B travel in the same direction at constant velocities of 15 m/s and 10 m/s, respectively. Pod A has a total length of 24 m, while Pod B has a total length of 16 m. From the instant the front end of Pod A aligns with the rear end of Pod B, how much time is required for Pod A to completely pass Pod B so that its rear end aligns with the front end of Pod B?

    • A) 1.6 s
    • B) 4.8 s
    • C) 8.0 s
    • D) 3.2 s
12. 12.

    An autonomous inspection robot travels along a straight, horizontal pipeline at a constant velocity, starting from the pipe entrance at time $t = 0\text{ s}$. After moving for 40 s, the robot is still 180 m away from reaching the midpoint of the pipeline. Continuing at the same velocity, at $t = 70\text{ s}$ from the start, it is located 60 m beyond the midpoint. What is the total length of the pipeline?

    • A) 1000 m
    • B) 500 m
    • C) 800 m
    • D) 640 m
13. 13.

    An autonomous inspection cart travels along a straight path directly toward a vertical barrier at a constant velocity of 20 m/s. The cart emits an ultrasonic pulse that travels at a constant speed of 340 m/s toward the barrier, reflects instantly, and is detected by the cart's onboard sensor 0.50 s after emission. What was the distance between the cart and the barrier at the moment the pulse was emitted?

    • A) 85 m
    • B) 90 m
    • C) 80 m
    • D) 95 m
14. 14.

    An automated production line places cylindrical parts onto a straight, horizontal conveyor belt at a constant rate of one part every 2.5 seconds. The conveyor moves with a constant velocity, keeping a steady distance of 1.2 meters between consecutive parts along the belt. At this operating speed, what distance does any individual part travel in 15.0 seconds?

    • A) 4.8 m
    • B) 6.0 m
    • C) 12.5 m
    • D) 7.2 m
15. 15.

    An automated testing cart moves along a straight horizontal track at a constant velocity. Two narrow optical sensors are positioned 15.0 m apart along the track, and the front bumper of the cart takes 2.5 s to travel between the two sensors. If the cart has an overall length of 0.90 m, for how many seconds does the cart block the beam of the first optical sensor?

    • A) 0.060 s
    • B) 0.10 s
    • C) 0.15 s
    • D) 0.36 s
16. 16.

    An automated transport cart moves along a straight rail at a constant velocity. A tracking system records that the cart travels from position 18 m to position 54 m in an elapsed time of 6.0 s. If the cart maintains this exact velocity throughout its motion, what was its position along the rail 5.0 s before it reached the 18 m mark?

    • A) -12 m
    • B) +48 m
    • C) +12 m
    • D) -6 m
17. 17.

    Two automated rovers, X and Y, travel toward each other along a straight horizontal track. At time $t = 0\text{ s}$, Rover X passes the $0\text{ m}$ mark traveling in the positive direction at a constant velocity of $4.0\text{ m/s}$, while Rover Y passes the $150\text{ m}$ mark traveling in the negative direction at a constant velocity of $-6.0\text{ m/s}$. At what position coordinate along the track do the two rovers pass each other?

    • A) $45\text{ m}$
    • B) $60\text{ m}$
    • C) $75\text{ m}$
    • D) $90\text{ m}$
18. 18.

    An autonomous ground shuttle and an aerial inspection drone travel along the same straight testing track in the same direction, each maintaining a constant velocity. The shuttle travels at 4.0 m/s and passes the starting marker at time $t = 0\text{ s}$. The drone passes the same starting marker 3.0 seconds later, traveling at a constant velocity of 7.0 m/s. At what distance from the starting marker does the drone overtake the shuttle?

    • A) 28 m
    • B) 21 m
    • C) 16 m
    • D) 36 m
19. 19.

    A robotic carrier operates along a straight horizontal track, traveling 18 m in the positive direction in 3.0 s and then immediately traveling 18 m in the negative direction during the next 3.0 s. A technician claims that the carrier executed constant velocity motion across the entire 6.0 s interval because it maintained a steady speed of 6.0 m/s throughout. Which statement correctly evaluates the technician's claim?

    • A) The claim is correct because covering equal distances in equal time intervals satisfies the complete definition of constant velocity motion.
    • B) The claim is incorrect because reversing the direction of motion altered the velocity, resulting in zero overall displacement across the interval.
    • C) The claim is correct because the average velocity over the total travel time equals the constant speed of 6.0 m/s.
    • D) The claim is incorrect because constant velocity motion requires the speed to change uniformly over time rather than remaining constant.
20. 20.

    An automated inspection vehicle travels along a straight track where an optical sensor system records its position at regular intervals. The vehicle is recorded at position 5 m at time 0 s, 11 m at 2.0 s, 17 m at 4.0 s, and 23 m at 6.0 s. Based on this data, which statement correctly evaluates the vehicle's motion?

    • A) It undergoes constant acceleration of 3 m/s² because its position increases by a steady amount in each interval.
    • B) It travels with an increasing velocity because its overall distance from the starting position grows over time.
    • C) It moves at a constant speed of 6 m/s because it covers a distance of 6 m between consecutive sensor readings.
    • D) It moves with a constant velocity of 3 m/s because equal displacements of 6 m occur during equal time intervals of 2.0 s.