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We use the uppercase Greek letter delta (Δ) to mean “change in” whatever quantity follows it; thus, Δ x means change in position (final position less initial position). We always solve for displacement by subtracting initial position x 0 from final position x f . Note that the SI unit for displacement is the meter, but sometimes we use kilometers or other units of length. Keep in mind that when units other than meters are used in a problem, you may need to convert them to meters to complete the calculation (see Appendix B ).

Objects in motion can also have a series of displacements. In the previous example of the pacing professor, the individual displacements are 2 m and −4 m, giving a total displacement of −2 m. We define total displacement     Δ x Total , as the sum of the individual displacements , and express this mathematically with the equation

Δ x Total = Δ x i ,

where Δ x i are the individual displacements. In the earlier example,

Δ x 1 = x 1 x 0 = 2 0 = 2 m.

Similarly,

Δ x 2 = x 2 x 1 = −2 ( 2 ) = −4 m.

Thus,

Δ x Total = Δ x 1 + Δ x 2 = 2 4 = −2 m ​.

The total displacement is 2 − 4 = −2 m to the left, or in the negative direction. It is also useful to calculate the magnitude of the displacement, or its size. The magnitude of the displacement is always positive. This is the absolute value of the displacement, because displacement is a vector and cannot have a negative value of magnitude. In our example, the magnitude of the total displacement is 2 m, whereas the magnitudes of the individual displacements are 2 m and 4 m.

The magnitude of the total displacement should not be confused with the distance traveled. Distance traveled x Total , is the total length of the path traveled between two positions. In the previous problem, the distance traveled    is the sum of the magnitudes of the individual displacements:

x Total = | Δ x 1 | + | Δ x 2 | = 2 + 4 = 6 m .

Average velocity

To calculate the other physical quantities in kinematics we must introduce the time variable. The time variable allows us not only to state where the object is (its position) during its motion, but also how fast it is moving. How fast an object is moving is given by the rate at which the position changes with time.

For each position x i , we assign a particular time t i . If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity     v . This vector quantity is simply the total displacement between two points divided by the time taken to travel between them. The time taken to travel between two points is called the elapsed time     Δ t .

Average velocity

If x 1 and x 2 are the positions of an object at times t 1 and t 2 , respectively, then

Average velocity = v = Displacement between two points Elapsed time between two points v = Δ x Δ t = x 2 x 1 t 2 t 1 .

It is important to note that the average velocity is a vector and can be negative, depending on positions x 1 and x 2 .

Delivering flyers

Jill sets out from her home to deliver flyers for her yard sale, traveling due east along her street lined with houses. At 0.5 km and 9 minutes later she runs out of flyers and has to retrace her steps back to her house to get more. This takes an additional 9 minutes. After picking up more flyers, she sets out again on the same path, continuing where she left off, and ends up 1.0 km from her house. This third leg of her trip takes 15 minutes. At this point she turns back toward her house, heading west. After 1.75 km and 25 minutes she stops to rest.

Questions & Answers

a length of copper wire was measured to be 50m with an uncertainty of 1cm, the thickness of the wire was measured to be 1mm with an uncertainty of 0.01mm, using a micrometer screw gauge, calculate the of copper wire used
Nicole Reply
If centripetal force is directed towards the center,why do you feel that you're thrown away from the center as a car goes around a curve? Explain
Maira Reply
Which kind of wave does wind form
Matthias Reply
calculate the distance you will travel if you mantain an average speed of 10N m/s for 40 second
Abdulai Reply
hw to calculate the momentum of the 2000.0 elephant change hunter at a speed of 7.50 m/s
Kingsley Reply
how many cm makes 1 inches
Hassan Reply
2.5
omwoyo
2.54cm=1inche
omwoyo
how do we convert from m/s to km/hr
Toni Reply
When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why?
SANA Reply
Explain why polarization does not occur in sound
Nuradeen
one ship sailing east with a speed of 7.5m/s passes a certain point at 8am and a second ship sailing north at the same speed passed the same point at 9.30am at what distance are they closet together and what is the distance between them then
Kuber Reply
density of a subtance is given as 360g/cm,put it in it s.i unit form
Linda Reply
if m2 is twice of m1. find the ration of kinetic energy in COM system to lab system of elastic collision
Raman Reply
What is a volt equal to?
Clifton Reply
list and explain the 3 ways of charging a conductor
Chidimma Reply
conduction convention rubbing
Asdesaw
formula of magnetic field
Yonas Reply
why polarization does not occur in sound
Nuradeen
Integral of a vector
Rahat Reply
define surface integral of a vector?
Rahat
Practice Key Terms 7

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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