A marker on a straight path has position x = -6 m. Which description matches?
A warehouse robot rolls along one straight aisle. The loading door is the origin: positions in front of the door count positive, positions behind it count negative. At 0 s the robot is 6 m in front of the door. Over the next 8 s it rolls back through the doorway, ending 4 m behind it.
A sensor logs the robot's position along the way. At 2 s the robot is 2 m in front of the door, so x = +2 m. At 4 s it is 2 m behind it, so x = −2 m.
One picture can show the whole log at once. Time runs along the horizontal axis in seconds. Position sits on the vertical axis in meters. A graph drawn this way is called a position-time graph.
It does the same job as the distance-time graphs you read in earlier grades, with one upgrade. Position can be negative as well as positive, so the line can dip below the time axis. A point below the axis means the object is on the negative side of the origin.
To find the robot's position at a stated time, run up from that time to the line, then across to the position axis. At t = 2 s the line sits at x = +2 m, so the robot is 2 m in front of the door.
The graph shows a forklift's position. What is the forklift's position at t = 4 s?
Run up from t = 4 s to the line, then across to the position axis.
The line sits at +2 m.
The forklift's position at t = 4 s is x = +2 m.
The graph shows a tide gauge float's position. What is the float's position, in m, at t = 6 s?
To find when the robot sits at a stated position, run the reading the other way: across from that position to the line, then down to the time axis. The line crosses x = −2 m at t = 4 s. That is the moment the robot is 2 m behind the door.
The graph shows a drone's position. At what time does the drone sit at x = −2 m?
Run across from −2 m to the line, then down to the time axis.
The falling segment passes −2 m at t = 7 s.
The drone reaches x = −2 m at t = 7 s.
The graph shows a glider's position. At what time, in s, is the glider at x = -3 m?
The graph shows a car's position along a test track. What is the car's position, in m, at t = 8 s?
The graph shows a lab cart's position. At what time, in s, does the cart reach x = -5 m?
The graph shows a remote sensor's position. At which time or times does the sensor sit at x = -2 m?