Unit 2.1 – Distance & Displacement

• Definition: Distance is the total path length covered by an object during its motion.
• Nature: It is a scalar quantity, meaning it has only magnitude and no direction.
• SI Unit: Meter (m).
• Key Points:
  • Always positive or zero.
  • Depends on the actual path taken.

• Definition: Displacement is the shortest distance between the initial and final positions of an object, along with its direction.
• Nature: It is a vector quantity, meaning it has both magnitude and direction.
• SI Unit: Meter (m).
• Key Points:
  • Can be positive, negative, or zero.
  • Independent of the path taken; depends only on the initial and final positions.

Quick Revision Points

• Distance: Total path length; scalar; always ≥ 0.
• Displacement: Shortest distance with direction; vector; can be positive, negative, or zero.
• Distance ≥ Magnitude of Displacement.
• If the motion is along a straight line without changing direction, Distance = Displacement.

Previous Year Questions and Answers

• Use Pythagoras theorem:
  $\text{Displacement}=\sqrt{(3^2+4^2)}=\sqrt{9+16}=\sqrt{25}=5\text{km}\mathrm{.}$
• Direction: North-east.

• Distance = Total path length = 10 km.
• Displacement = 0 (as the car returns to the starting point).

• Distance = 5 m (A to B) + 5 m (B to A) = 10 m.
• Displacement = 0 (as the particle returns to the starting point).

• Net displacement = 6 km (east) − 8 km (west) = −2 km (west).
• Magnitude = 2 km, Direction = West.

• Distance = 400 m (total path length).
• Displacement = 0 (as he returns to the starting point).

Expected Questions

• Use Pythagoras theorem:
  $\text{Displacement}=\sqrt{({12}^2+5^2)}=\sqrt{144+25}=\sqrt{169}=13\text{km}\mathrm{.}$

• Distance = Half the circumference = $𝜋𝑟=\frac{22}{7}\times 7=22\text{m}\mathrm{.}$
• Displacement = Diameter = $2𝑟=2\times 7=14\text{m}\mathrm{.}$

• Net east-west displacement = 5 km (east) − 5 km (west) = 0.
• Net north-south displacement = 3 km (north).
• Resultant displacement = 3 km (north).