Difference Between Distance and Displacement with Definition, Examples, MCQs, Q&A, FAQs, Worksheet, Test Paper

ANAND CLASSES study material and notes to learn the key differences between distance and displacement in physics. Understand their definitions, properties, formulas, and graphical representation with examples.

📌 Distance

✅ Definition: Distance is the actual path length covered by a moving particle in a given interval of time.
✅ Key Features:

• Always positive and never decreases.
• Scalar Quantity (Has only magnitude, no direction).

• Formula: If a particle starts from A and reaches C through B, then: 🏃‍♂️ Distance traveled = AB + BC = 7 m
• Dimension: 📏 [M⁰L¹T⁰]
• SI Unit: 🏅 Metre (m)

📌 Displacement

✅ Definition: Displacement is the shortest distance between the initial and final position of a particle in a given time.
✅ Key Features:

• Vector Quantity (Has both magnitude and direction).

• Formula: Displacement of the particle from A to C is given by: 📐 |AC| = √[(AB)² + (BC)² + 2(AB)(BC)cos90°] = 5m
• Dimension: 📏 [M⁰L¹T⁰]
• SI Unit: 🏅 Metre (m)
• Vector Addition Rule: If a body undergoes multiple displacements S₁, S₂, S₃, …, Sₙ, then the net displacement is: 🧮 S = S₁ + S₂ + S₃ + … + Sₙ

Difference Between Distance and Displacement

Here is a clear tabular comparison between distance and displacement:

Note : The magnitude of displacement is equal to minimum possible distance between two positions. So

Distance ≥ |Displacement|.

Graphical illustration of Distance and Displacement

Here is a graphical illustration of distance and displacement. The curved path APB represents the actual distance traveled, while the straight arrow from A to B represents the displacement vector r_AB​

Imagine a particle moving from point A to point B along a curved path APB.

• Distance (s): The total length of the path APB traveled by the particle.
• Displacement r_AB: The straight-line vector from A to B.
• r_AB = r_B – r_A

🎯 Question-Answer Format for JEE, NEET, and CBSE Board Class 11 Exams

❓ Q1: Define distance and displacement. Give an example.

🔹 Ans:

• Distance: The actual path covered by a particle.
• Displacement: The shortest distance between the initial and final position.
• Example: A person walks 4 m east and then 3 m north.
  • 🏃‍♂️ Distance traveled = 4 + 3 = 7 m
  • 📐 Displacement = √(4² + 3²) = 5 m

❓ Q2: Can displacement be greater than distance?

🔹 Ans: No, displacement is always lesser than or equal to distance.

❓ Q3: If a body returns to its starting point, what is the displacement?

🔹 Ans: Zero, because the initial and final positions coincide.

❓ Q4: State the unit and dimension of distance and displacement.

🔹 Ans:

• SI Unit: 🏅 Metre (m)
• Dimension: 📏 [M⁰L¹T⁰]

🎯 MCQs with Answers and Explanation

✅ Q1: Which of the following statements is correct?

A) Distance is always greater than or equal to displacement.
B) Displacement is always greater than distance.
C) Distance and displacement are always equal.
D) Distance can be negative.

✔️ Answer: A) Distance is always greater than or equal to displacement.

📝 Explanation: Displacement is the shortest path, while distance is the actual path.

✅ Q2: A person walks 3 m east and then 4 m north. What is the displacement?

A) 5 m
B) 7 m
C) 3.5 m
D) 4.5 m

✔️ Answer: A) 5 m

📝 Explanation: Displacement is calculated using Pythagoras’ theorem: √(3² + 4²) = 5 m

✅ Q3: Which of the following is a vector quantity?

A) Distance
B) Speed
C) Displacement
D) Time

✔️ Answer: C) Displacement

📝 Explanation: Displacement has both magnitude and direction, making it a vector.

💡 Conceptual Questions with Answers

❓ Q1: Can a body have zero displacement but nonzero distance?

🔹 Ans: Yes, when it returns to its starting point.

❓ Q2: Why is displacement always a straight line?

🔹 Ans: Because it is the shortest path between two points.

❓ Q3: Can displacement be negative?

🔹 Ans: No, but it can have a direction opposite to reference.

🚀 Do You Know?

• 📌 Distance is path-dependent, while displacement is not.
• 📌 The magnitude of displacement can never be greater than distance.
• 📌 If velocity is constant in a straight line, distance and displacement are equal.

📝 Worksheet

1️⃣ Define distance and displacement with examples.
2️⃣ A car travels 5 km east, then 12 km west. Calculate displacement.
3️⃣ A boy runs in a circular track of radius 7 m and completes one round. Find distance and displacement.
4️⃣ A particle moves 3 m north, 4 m east. Find distance and displacement.
5️⃣ Explain why displacement is a vector and distance is a scalar.

🏆 Test Paper (Total: 10 Marks)

1️⃣ Define distance and displacement. (2 marks)
2️⃣ A cyclist moves 6 m north, then 8 m east. Find displacement. (2 marks)
3️⃣ Differentiate between distance and displacement. (2 marks)
4️⃣ A car moves 10 km east, then returns 4 km west. Find distance and displacement. (2 marks)
5️⃣ Explain the conditions when displacement equals distance. (2 marks)

📌 Quick Revision Points

• Distance: 🏃‍♂️ Actual path covered, scalar quantity.
• Displacement: 📐 Shortest path, vector quantity.
• Distance ≥ Displacement
• Dimension: 📏 [M⁰L¹T⁰]
• SI Unit: 🏅 Metre (m)
• If a body returns to its starting position, displacement = 0

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