Doubt Calculating the Total Displacement for this Person Walking

[Remle]

Homework Statement

You start walking home from school. After walking 1.3 km North, you get a phone call on your cell from your mom asking if you can meet her at the mall. You will have to turn around and walk 2.5 km South. Determine your distance and displacement to get to the mall.

Relevant Equations

d=df-di

I having a little bit of problem with ##\Delta d = d_f - d_i##. When substituting fo ##d_f## and ##d_i##, should I follow the signs rule (positive or negative)?
For example,
The problem shows that the displacement is ##1.2~\rm{km}, south## by solving ##\Delta d = -2.5 + 1.3## and I get that, but if I use the formula above the equation would appear like this ##\Delta d = -2.5 - 1.3## which gives me ##-3.8~\rm{km}## or ##3.8~\rm{km}, south##.

What am I missing?

source: http://www.studyphysics.ca/2007/20/01_kinematics/08_velocity.pdf

 

[kuruman]

There are two displacements, one is 1.3 km North and the other is 2.5 km South. The overall displacement is the sum of the two. Note that the displacements have opposite directions so you are adding a positive and a negative number.

 

[Remle]

There are two displacements.

THIS is what I needed. So first displacement is ##\Delta d = 1.3 - 0## and the second is ##\Delta d = 0 - 2.5## so to speak.

 

[PeroK]

THIS is what I needed. So first displacement is ##\Delta d = 1.3 - 0## and the second is ##\Delta d = 0 - 2.5## so to speak.

If you are given two points (a start point and an end point), then the dispalcement is the position vector of the end point minus the position vector of the start point.

But, in this case you are given the displacements, so there is no need for any subtraction:
$$\Delta d_1 = 1.3km, \ \Delta d_2 = - 2.5km$$

 

[berkeman]

@Remle -- what did you get for the distance answer?

 

[Remle]

@Remle -- what did you get for the distance answer?

Sorry for the late response. For the distance since is a scalar just had to add all the numbers. ##d = 1.3 + 2.5 = 3.8~\rm{km}##.

 

[haruspex]

Sorry for the late response. For the distance since is a scalar just had to add all the numbers. ##d = 1.3 + 2.5 = 3.8~\rm{km}##.

No, distance is not a scalar, it is a magnitude. Scalars have sign.
Taking North as positive you can find displacement using scalars: 1.3km+(-2.5)km N = -1.2km N, or 1.2km S.
For distances you add the magnitudes |1.3|+|-2.5|=3.8.