Worksheet: Position, Distance, and Displacement

In this worksheet, we will practice calculating the displacement vector and the scalar distance between two points.

Q1:

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?

Q2:

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?

  • A ( 5 . 0 ) i km
  • B ( 2 . 0 ) i km
  • C ( 5 . 0 ) i km
  • D ( 2 . 5 ) i km
  • E ( 2 . 5 ) i km

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

  • A ( 2 . 5 ) i km
  • B ( 2 . 0 ) i km
  • C ( 2 . 5 ) i km
  • D ( 2 . 0 ) i km
  • E ( 5 . 0 ) i km

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?

  • Awest
  • Beast
  • Cnorth
  • Dsouth
  • Ezero displacement

Q3:

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?

  • A 1 4 i m
  • B 1 0 i m
  • C 1 6 i m
  • D 1 6 i m
  • E 6 i m

Q4:

A long measuring stick rests against a wall in a physics laboratory and its end with the 200 cm mark is on the floor. A ladybug lands on the 100 cm mark and crawls randomly along the stick. It first walks 15 cm toward the floor, then it walks 56 cm toward the wall, then it walks 3 cm toward the floor again. Then, after a brief stop, it continues for 25 cm toward the floor and then, again, it crawls up 19 cm toward the wall before coming to complete rest.

State the ladybug’s displacement vector from its starting position, assuming that displacement in the direction u along the stick’s length away from the wall and toward the floor corresponds to positive values.

  • A 3 2 u cm
  • B 6 8 u cm
  • C 6 0 u cm
  • D 6 8 u cm
  • E 3 2 u cm

Find the magnitude of the displacement of the ladybug along the stick’s length from the floor.

Q5:

On a journey, a cyclist rides 3.0 km west and then turns around and rides 2.0 km east. Assume that east corresponds to positive displacement.

What is the cyclist’s displacement from the starting point of their journey to its end point?

What distance does the cyclist travel during their journey?

What is the magnitude of the cyclist’s displacement from the starting point of their journey to its end point?

Q6:

Which of the following statements comparing position, distance, and displacement is correct?

  • AAn object may record a nonzero distance while maintaining a position of zero.
  • BAn object may record a distance of zero while recording a nonzero displacement.
  • CAn object may record a nonzero distance while recording a displacement of zero.
  • DAn object may record a nonzero displacement while maintaining a position of zero.

Q7:

The diagram shows the paths of four particles moving along the 𝑥-axis.

What is the distance traveled by particle 𝐷?

What is the magnitude of the displacement of particle 𝐷 from start to finish?

What is the displacement of particle 𝐷 from start to finish?

Q8:

The diagram shows the paths of four particles moving along the 𝑥-axis.

What is the distance traveled by particle 𝐶?

What is the magnitude of the displacement of particle 𝐶 from start to finish?

What is the displacement of particle 𝐶 from start to finish?

Q9:

The diagram shows the paths of four particles moving along the 𝑥-axis.

What is the distance traveled by particle B?

What is the magnitude of the displacement of particle B from start to finish?

What is the displacement of particle B from start to finish?

Q10:

The diagram shows the paths of four particles moving along the 𝑥-axis.

What is the distance traveled by particle 𝐴?

What is the magnitude of the displacement of particle 𝐴 from start to finish?

Q11:

The map given shows the blocks of a city. Each block is a square, with each side being 120 m long. Line 𝐴 shows the path taken by a tourist walking through the city.

How far does the tourist walk?

What is the magnitude of the displacement from start to finish? Round your answer to the nearest meter.

What is the angle in degrees, east of north, of the displacement from start to finish? Give your answer to 3 significant figures.

Q12:

The map given shows the blocks of a city. Each block is a square with each side being 160 m long. Line 𝐵 shows the path taken by a tourist walking through the city.

How far does the tourist walk? Give your answer in meters.

What is the magnitude of the displacement from start to finish? Round your answer to the nearest meter.

What is the angle in degrees, east of north, of the displacement from start to finish? Give your answer to 3 significant figures.

Q13:

The map shows the paths walked by hikers through a forest. Hiker 1 walks along path 1 and hiker 2 walks along path 2. (For each part of the question, give your answer in kilometers to 3 significant figures.)