Worksheet: Distance and Displacement

In this worksheet, we will practice how to define distance as the length of a path between two positions and to define displacement as the straight line distance between two positions.

Q1:

A rover on Mars is initially facing north. The rover travels 300 m in the direction it is facing, turns to its left and travels 200 m in this new direction, turns left again and travels 500 m in the direction it is now facing, and turns left once more and travels 100 m in the direction that it is now facing.

What is the rover’s net displacement east of its initial position?

What is the rover’s net displacement north of its initial position?

Q2:

A woman starts at the point A shown in the diagram and walks up two flights of stairs that are both 6 m in height and walks to point B, which is directly above point A.

What is the woman’s upward vertical displacement?

What is the woman’s net horizontal displacement?

Q3:

A tourist wandering around a city walks 965 m east, then 244 m south, then 139 m west, then 760 m north, then 826 m west, and then finally 44 m south before stopping for a rest. How far is the tourist displaced from the point they started walking from?

Q4:

A bird flies 2.5 km north, then 4 km west, then 1 km south, then 3 km east, and finally 2 km north.

What is the bird’s net displacement north from its starting position?

What is the bird’s net displacement west from its starting position?

Q5:

A vertically upward pointing ladder has rungs that are spaced 15 cm apart, with the first rung 15 cm above the ground. A construction worker climbs eight rungs up the ladder and then climbs down two rungs. How many centimeters above the ground are the worker’s feet displaced?

Q6:

A ship sails 7.5 km west and then 10 km east.

What is the distance moved by the ship?

What is the ship’s net displacement to the west from its starting position?

Q7:

A leaf is blown by the wind. The leaf moves 5 m forward and then 3 m backward.

What is the distance moved by the leaf?

What is the leaf’s net forward displacement?

Q8:

A car travels 6 km north and then 8 km south. What is the car’s net displacement to the north from its starting position?

Q9:

A horse in a field moves 20 m to the east and 5 m to the west. What is the horse’s net distance to the east from its starting position?

Q10:

To help track how much exercise they do, a person wears a device that counts the number of steps they take. At the end of the day, the device recorded that 5,673 steps had been taken. The person measures their stride length as 0.48 m. What distance did the person walk? State your answer to the nearest meter.

Q11:

What is the total distance walked by someone along the lines shown in the diagram?

Q12:

A speedboat passes by markers at the points A, B, and C, as shown in the diagram. Positive displacement is considered to be away from A, toward C.

What is the boat’s displacement from A when it is at B?

What is the boat’s displacement from C when it is at B?

What is the boat’s displacement from A when it is at C?

What is the boat’s displacement from C when it is at A?

Q13:

A person walks from point A, shown in the diagram, to point B.

What is the displacement of point B from point A in the 𝑥-direction?

What is the displacement of point B from point A in the 𝑦-direction?

Q14:

What is the total distance covered by someone who walks along the lines shown in the diagram?

Q15:

What is the total distance covered by someone who walks along the lines shown in the diagram, not walking on any line more than once?

Q16:

Two people walk along triangular lines that connect the points 𝐴, 𝐵, and 𝐶 shown in the diagram. The first person walks from point 𝐴 along a triangular path that returns them to point 𝐴. When the first person returns to point 𝐴, they stop. The second person walks from point 𝐵 along a triangular path that returns them to point 𝐵. When the second person returns to point 𝐵, they stop.

What is the displacement of the first person from point 𝐴 in the 𝑥-direction when they stop?

What is the displacement of the first person from point 𝐴 in the 𝑦-direction when they stop?

What is the displacement of the second person from point 𝐵 in the 𝑥-direction when they stop?

What is the displacement of the second person from point 𝐵 in the 𝑦-direction when they stop?

Q17:

A person walks from point 𝐴, shown in the diagram, to point 𝐵.

What is the displacement of point 𝐵 from point 𝐴 in the 𝑥-direction?

What is the displacement of point 𝐵 from point 𝐴 in the 𝑦-direction?

Q18:

What is the total distance covered by someone who walks along the lines shown in the diagram?

Q19:

What is the total distance covered by someone who walks along the lines shown in the diagram?

Q20:

A person walks from the point 𝐴, shown in the diagram, to the point 𝐵.

What is the displacement of point 𝐵 from point 𝐴 in the 𝑥-direction?

What is the displacement of point 𝐵 from point 𝐴 in the 𝑦-direction?

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