A particle moves `3 m` north , then `4 m` east and finally ` 6m` south . Calculate the distance travelled and the displacement.

Options

A. 12 m, 7 m
B. 13 m, 5 m
C. 13 m, 13 m
D. None of these

Answer

B

Explanation

As shown in Fig., the particle starts from `O` and moves `3 m` north `( = OA)m` east ( = AB) , and `6 m` south `( = Bc)`.
Distance travelled
` = OA + AB + BC`
` = 3 m + 4 m + 6 m`
` = 13 m`
Displacement `= vec ( OC)` ,
where `OC = | vec (OC )| = sqrt( OD^(2) + DC^(2)) = sqrt( AB^(2) + (BC - BD)^(2))`
` sqrt( 4^(2) + ( 6 - 3)^(2)) = 5 m`