Net Displacement: Subtracting E from W Direction Vectors

In summary, the direction of the position vectors being subtracted does not matter as long as they are parallel. However, it is important to note that 10 units W is equivalent to -10 units E. The physical interpretation of adding or subtracting position vectors is the total distance traveled, regardless of direction.
  • #1
ybhathena
42
0
Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?
 
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  • #2
ybhathena said:
Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?
They must be treated as vectors. 10 units E minus 10 units W does not equal zero, if that's what you're thinking. (You can only subtract components that are along the same direction.)
 
  • #3
If they are in opposite directions, you can subtract. If E and W mean East and West, you can subtract.
 
  • #4
mathman said:
If they are in opposite directions, you can subtract. If E and W mean East and West, you can subtract.
Good point! For some reason, I was thinking of East and South, but I'm sure you're right that it means East and West. Good catch. (Oops!)
 
  • #5
ybhathena said:
Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?
Let me answer it again, given mathman's clarification:

Yes, you can subtract them since they are parallel. But realize that 10 units W is the same as -10 units E. So 10 E - 10 W = 10 E - (-10 E) = 20 units E.

Make sense?

(Glad that mathman was awake.)
 
  • #6
ybhathena said:
Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?
In your mind, what is the physical interpretation of the addition/subtraction of such position vectors?
 
  • #7
If I drive 10 miles east, turn around, put the car in reverse and drive another 10 miles while facing west, the result is 20 miles traveled to the east.
 

1. What is net displacement?

Net displacement is the overall change in position or location of an object or particle, taking into account both magnitude and direction.

2. How is net displacement calculated?

Net displacement can be calculated by subtracting the east (E) direction vector from the west (W) direction vector. This results in a single vector representing the overall displacement.

3. Why is it important to consider both magnitude and direction in net displacement?

In order to accurately describe the change in position of an object, both magnitude and direction must be taken into account. This allows for a more precise and comprehensive understanding of the object's movement.

4. Can net displacement be negative?

Yes, net displacement can be negative. This occurs when the east and west direction vectors are in opposite directions, resulting in a negative value for the overall displacement.

5. What units are used to measure net displacement?

Net displacement is typically measured in units of length, such as meters or kilometers.

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