Question

a train engineer drives a train 235 km north along a straight track . then he drives the train back south 126 km . finally , he drives north again 45.0 km to his final destination . what is the engineer total displacement .

Answer 1

let here North direction is along +Y and South direction is along -Y

similarly East direction is towards +X and west direction is towards -X

now it is given that

first it moves 235 km north

$d_1 = 235 \hat j$

then it moves back 126 km south

$d_2 = - 126 \hat j$

then again he moves north

$d_3 = 45 \hat j$

now the total displacement is given as

$d = d_1 + d_2 + d_3$

$d = 235 - 126 + 45 = 154 km$

so final displacement of train is 154 km North