Doubt Calculating the Total Displacement for this Person Walking

  • #1
Remle
12
8
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
 
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  • #2
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.
 
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  • #3
kuruman said:
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.
 
  • #4
Remle said:
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:
$$\Delta d_1 = 1.3km, \ \Delta d_2 = - 2.5km$$
 
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  • #5
@Remle -- what did you get for the distance answer?
 
  • #6
berkeman said:
@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}##.
 
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  • #7
Remle said:
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.
 

FAQ: Doubt Calculating the Total Displacement for this Person Walking

What is displacement in the context of walking?

Displacement refers to the shortest straight-line distance from the starting point to the ending point of a person's walk, regardless of the path taken. It is a vector quantity, meaning it has both magnitude and direction.

How do you calculate the total displacement?

To calculate the total displacement, you need to determine the straight-line distance between the starting and ending points of the walk. This can be done using the Pythagorean theorem if the path involves right angles or by vector addition if the path is more complex.

What tools or methods can be used to measure displacement?

Displacement can be measured using tools like GPS devices, which provide coordinates for the starting and ending points, or by mapping out the walk on a grid and using mathematical calculations such as the Pythagorean theorem or trigonometric functions.

Does the path taken affect the total displacement?

No, the path taken does not affect the total displacement. Displacement depends only on the initial and final positions, not on the route traveled between them.

Can displacement ever be greater than the distance traveled?

No, displacement can never be greater than the distance traveled. The distance traveled is the length of the actual path taken, which is always equal to or greater than the straight-line displacement between the starting and ending points.

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