medium difficulty7 min

Distance and Displacement

Distance is the total length of the actual path travelled. Displacement is the shortest straight-line change in position from the initial point to the final point, with direction.

In one line: Distance follows the road; displacement points from start to finish.

Practice This Concept

Understand it

Distance is a scalar quantity, so it has magnitude only. Displacement is a vector quantity, so direction matters. Distance can never be less than displacement in magnitude; they are equal only when motion is along a straight line without changing direction.

Example

If a student walks 3 m east and then 4 m west, distance is 7 m, but displacement is 1 m west.

Rule to remember

Distance = total path length.

Displacement = final position minus initial position along a chosen direction.

Magnitude of displacement is less than or equal to distance.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A girl walks 6 m north and then returns 2 m south.

1Distance = 6 + 2 = 8 m.
2Displacement = 4 m north, because her final position is 4 m north of the starting point.

Method you can reuse

1Write each part of the path for distance and add all lengths.
2For displacement, mark initial and final positions, choose direction, and find the straight-line change in position.

Visual tip

A line or path diagram can show actual route length and a straight arrow from starting point to final point.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

When can distance and displacement have the same magnitude?

Think first, then show answer

Distance and displacement have the same magnitude when the object moves along a straight path in one direction without turning back.

Common wrong answer

Writing displacement as 8 m in the worked example.

Why it loses marks: 8 m is the total path length, not the net change in position.

Don't mix this up

Students often add directions like east and west as if both distance and displacement are the same type of quantity.

Exam tip

For displacement, mark the starting point and ending point first; the actual route matters for distance, not for displacement.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Students may be given movements along a line or around a rectangle and asked to calculate distance and displacement separately.

1
Enough for 1 mark
Distance is the total length of the actual path travelled. Displacement is the shortest straight-line change in position from the initial point to the final point, with direction.
2
Add for 2 marks
Distance is a scalar quantity, so it has magnitude only.
3
Add for 3 marks
Displacement is a vector quantity, so direction matters.

MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results