Position–time graphs Transitional Reasoning Download PDF

Questions

1. 1.

   Two automated inspection drones travel along a straight overhead rail parallel to the x-axis. At $t = 0\text{ s}$, Drone 1 is located at $x = 0\text{ m}$ and Drone 2 is located at $x = 100\text{ m}$. Their position–time graphs are both straight lines that intersect at $t = 20\text{ s}$ at the position $x = 60\text{ m}$. Based on these graphs, which statement correctly describes the motion of the drones?

   • A) At $t = 20\text{ s}$, both drones have the same instantaneous velocity because their position–time graphs intersect.
   • B) Drone 1 travels with a greater speed than Drone 2 throughout the 20-second interval.
   • C) Drone 2 covers a greater distance than Drone 1 during the 20-second interval.
   • D) Drone 2 moves with a positive velocity because its position coordinate remains positive throughout the motion.
2. 2.

   Two automated inspection pods, Alpha and Beta, travel along a straight calibrated track parallel to the x-axis. From $t = 0\text{ s}$ to $t = 10\text{ s}$, Alpha's position–time graph is a straight line connecting $(0\text{ s}, 0\text{ m})$ to $(10\text{ s}, 20\text{ m})$. Over the same interval, Beta's position–time graph begins at $(0\text{ s}, 0\text{ m})$, smoothly rises to a crest at $x = 35\text{ m}$ at $t = 6\text{ s}$, and descends to end at $(10\text{ s}, 20\text{ m})$. Based on their position–time graphs over this 10-second test, which statement correctly compares the motion of the two pods?

   • A) Pod Beta has a greater average velocity than Pod Alpha because it achieves a significantly higher coordinate on the position axis.
   • B) Pod Alpha traveled a greater total distance than Pod Beta because its graph shows continuous motion in one direction without turning around.
   • C) Both pods have the same average velocity over the 10-second interval, but Pod Beta has a greater average speed.
   • D) At $t = 6\text{ s}$, Pod Beta has a greater instantaneous velocity than Pod Alpha because its position coordinate reaches its peak value.
3. 3.

   A motion sensor records the one-dimensional movement of an automated rover along a straight track calibrated along the x-axis. The rover's position–time graph begins at x = +4 m at t = 0 s, crosses the time axis at t = 2 s, reaches a smooth minimum turning point at x = -6 m at t = 5 s where the tangent is horizontal, and returns to x = 0 m at t = 8 s. Based on this position–time data, which statement correctly evaluates the rover's motion?

   • A) The rover momentarily comes to rest at t = 2 s because its position graph crosses the time axis.
   • B) The average speed of the rover over the entire 8-second interval is 0.5 m/s.
   • C) The rover moves in the negative direction throughout the entire 8-second interval.
   • D) The magnitude of the rover's average velocity over the 8-second interval is 0.5 m/s, and its instantaneous velocity is directed in the positive direction between t = 5 s and t = 8 s.
4. 4.

   A telemetry unit records the one-dimensional motion of an electric transit car along a straight track relative to a station entrance at x = 0 m. The resulting position–time graph shows the car remaining stationary at x = -20 m from t = 0 s to t = 2 s, curving upward with an increasingly steep positive slope until it reaches x = 0 m at t = 6 s, and continuing as a straight line with that constant positive slope to x = +40 m at t = 10 s. Based on this graph, which deduction regarding the car's motion is correct?

   • A) The transit car is at rest at t = 6 s because its position coordinate equals zero at that instant.
   • B) The transit car accelerates in the positive direction between t = 2 s and t = 6 s, and then maintains a constant velocity from t = 6 s to t = 10 s.
   • C) The transit car's average velocity over the entire 10-second interval is greater than its instantaneous velocity at t = 8 s.
   • D) The transit car reverses its direction of travel at t = 6 s as its position coordinate changes from negative to positive values.
5. 5.

   An engineer analyzes the one-dimensional motion of a maglev carriage along a straight test track. Between $t = 2\text{ s}$ and $t = 6\text{ s}$, the carriage's position–time graph lies entirely above the time axis, exhibits a negative slope at every point, and curves upward with decreasing steepness. Which statement correctly describes the motion of the carriage during this interval?

   • A) The carriage is moving in the negative direction and speeding up because both its velocity and acceleration are negative.
   • B) The carriage is moving in the negative direction and slowing down because its velocity is negative while its acceleration is positive.
   • C) The carriage is moving in the positive direction and speeding up because its upward curvature indicates a positive velocity.
   • D) The carriage is moving in the positive direction and slowing down because its position is positive while its slope decreases.
6. 6.

   Two automated inspection shuttles, P and Q, move along a straight track starting from the same initial position at $t = 0\text{ s}$. Shuttle P's position–time graph is a straight line with a constant positive slope, while Shuttle Q's graph is a curve that starts with zero slope at $t = 0\text{ s}$, curves upward with steadily increasing steepness, and intersects Shuttle P's line at $t = 6\text{ s}$. Based on their position–time graphs, which statement correctly describes the motion of the two shuttles?

   • A) At $t = 6\text{ s}$, both shuttles have equal instantaneous velocities because their position–time graphs intersect.
   • B) Shuttle Q has a greater instantaneous velocity than Shuttle P at every point between $t = 0\text{ s}$ and $t = 6\text{ s}$.
   • C) Shuttle Q has a greater average velocity than Shuttle P over the entire time interval from $t = 0\text{ s}$ to $t = 6\text{ s}$.
   • D) At an instant between $t = 0\text{ s}$ and $t = 6\text{ s}$, the tangent to Shuttle Q's curve has the same slope as Shuttle P's line, meaning their instantaneous velocities are equal before they meet.
7. 7.

   A logistics robot navigates a straight corridor with its position monitored along a linear track over a 10-second test. From t = 0 s to t = 4 s, its position–time graph is a curve starting at x = 0 m whose slope steadily decreases until it becomes horizontal at x = +8 m. From t = 4 s to t = 10 s, the graph is a straight line that connects position x = +8 m directly to x = -4 m. Based on this position–time data, which statement correctly describes the robot's motion?

   • A) The robot moves at a constant positive velocity between t = 0 s and t = 4 s.
   • B) The total distance traveled by the robot over the 10-second test is 4 m.
   • C) The robot momentarily comes to rest at t = 4 s before traveling in the negative direction at a constant speed of 2 m/s.
   • D) The robot returns to its initial reference position at the end of the 10-second test.
8. 8.

   A remote-controlled cart moves along a straight east-west track where eastward is defined as the positive direction. A sensor records that the cart travels from 0 m to +12 m at a constant rate over the first 4 s, remains stationary at +12 m for 2 s, and then travels at a constant rate to -6 m over the next 6 s. Based on this motion, which statement correctly describes the cart's velocity?

   • A) The cart has a greater speed during the final 6 s than during the first 4 s because it reaches a negative coordinate.
   • B) The cart's average velocity across the entire 12 s trip is directed eastward because it spent most of the time at positive positions.
   • C) The cart reverses its direction of travel at t = 4 s as soon as it ceases its eastward motion.
   • D) The cart moves eastward at 3 m/s during the first 4 s and westward at 3 m/s during the final 6 s.