Lesson: Position, Distance, and Displacement


In this lesson, we will learn how to calculate the displacement vector and the scalar distance between two points.



Sample Question Videos

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  • 03:12
  • 02:31



A scuba diver makes a slow descent into the depths of the ocean. His vertical position with respect to a boat on the surface changes several times. He makes the first stop 9.0 m from the boat but has a problem with equalizing the pressure, so he ascends 3.0 m and then continues descending for another 12.0 m to the second stop. From there, he ascends 4 m and then descends for 18.0 m, ascends again for 7 m and descends again for 24.0 m, where he makes a stop, waiting for his buddy. What is his distance to the boat?


A car is 2.0 km west of a traffic light at the instant 𝑡=0min and 5.0 km east of the same traffic light at 𝑡=6.0min. Assume the origin of the coordinate system is the traffic light and the positive 𝑥-direction corresponds to eastward.

What is the car’s position vector at 𝑡=0min?

What is the car’s position vector at 𝑡=6.0min?

What is the magnitude of the car’s displacement between 𝑡=0min and 𝑡=6.0min?

What is the direction of the car’s displacement between 𝑡=0min and 𝑡=6.0min?


A cave diver enters a long straight underwater tunnel. When the diver’s displacement from the point at which she has entered the tunnel is 20 m, she accidentally drops her camera, which she does not notice until she has moved 6 m farther into the tunnel, moving in the same direction as before. When she notices her camera is missing, she swims back in the opposite direction to her original motion, traveling 10 m. The diver fails to find the camera and so she decides to end the dive.

What is the diver’s distance from the tunnel’s entry point when she decides to end the dive?

Taking the tunnel’s entry point as the origin of a one-dimensional coordinate system where the positive direction corresponds to the direction toward the tunnel origin relative to positions within the tunnel, what is the diver’s displacement vector when she decides to end the dive?

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