Question

If North is the positive direction, supposing one person walks towards north direction for 5m, then this person walks backwards to the South direction for 10m, what is the total travel distance for this person? what is the displacement for this person?

a. -15m

b. 15m

c. 5m

d. -5m

Answer 1

It must be noted that distance is a scalar quantity. Because of this reason, it only has the magnitude and no direction. Hence, it would always be positive, irrespective of the fact that either it is moving in +ve direction or in -ve direction.

When a person goes in north direction, let the distance be s1.

Given s1 = 5 m

When he returns and goes to south direction, say the distance covered is s2, given as

s2 = 10 m

Hence, total distance , s = s1+s2  

= 5+10

s = 15 m

Let us now talk about displacement, it is a vector quantity i.e having both magnitude as well as direction. Hence, it can be positive or negative and even zero.

Since north is assumed to be positive direction, hence the displacement (say D1) is given by

D1 = + 5 m

When it goes back to south, it is travelling in negative direction, hence, displacement D2 is given by

D2 = -10 m

Total displacement, D = D1 + D2

= 5 - 10

D = -5 m

i.e total distance covered by the man is 15 m, however the displacement is -5 m.