Question

A particle moves $3m$ north, then $4m$ east and finally $6m$ south. Which of the following is correct about the distance travelled and the displacement?

• A. The distance travelled is $13m$.
• B. The distance travelled is $12m$.
• C. The displacement is $13m$.
• D. The displacement is $5m$.

Answer 1

Answer: (A), (D)

The correct options are
A

The distance travelled is $13m$.

D

The displacement is $5m$.

Let the particle start from $A$ and finally reached $B$ as shown. Distance is the length of the actual path taken by it.
In this case, distance $=3+4+6=13m$

Displacement is the shortest distance between the initial and final position.
In this case, displacement $=AB$
$=\sqrt{(B{C}^2+A{C}^2)}$ [Pythagoras Theorem]
$=\sqrt{(3^2+4^2)}=5m$