Question

A particle moves from A to P and then it moves from P to B as shown in the figure. Find path length and displacement.

• A. $\frac{2l}{\sqrt{3}},l$
• B. $\frac{l}{\sqrt{3}},l$
• C. $2l,l$
• D. $l,\frac{2l}{\sqrt{3}}$

Answer 1

The correct option is A $\frac{2l}{\sqrt{3}},l$

In triangle APB

$\angle APB={120}^o,AP=BP=x$

using cosine formula

$cos\angle APB=\frac{A{P}^2+B{P}^2-A{B}^2}{2\times AP\times BP}$

$-\frac{1}{2}=\frac{2x^2-l^2}{2x^2}$

$x=\frac{l}{\sqrt{3}}$

Path length=$AP+BP=2x=\frac{2l}{\sqrt{3}}$

displacement=$AB=l$