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  1. What is Jill’s total displacement to the point where she stops to rest?
  2. What is the magnitude of the final displacement?
  3. What is the average velocity during her entire trip?
  4. What is the total distance traveled?
  5. Make a graph of position versus time.

A sketch of Jill’s movements is shown in [link] .

Figure shows a timeline of a person’s movement. First displacement is from the home to the right by 0.5 kilometers. Second displacement is back to the starting point. Third displacement is to the right by 1.0 kilometer. Fourth displacement is from the final point to the left by 1.75 kilometers.
Timeline of Jill’s movements.

Strategy

The problem contains data on the various legs of Jill’s trip, so it would be useful to make a table of the physical quantities. We are given position and time in the wording of the problem so we can calculate the displacements and the elapsed time. We take east to be the positive direction. From this information we can find the total displacement and average velocity. Jill’s home is the starting point x 0 . The following table gives Jill’s time and position in the first two columns, and the displacements are calculated in the third column.

Time t i (min) Position x i (km) Displacement Δ x i (km)
t 0 = 0 x 0 = 0 Δ x 0 = 0
t 1 = 9 x 1 = 0.5 Δ x 1 = x 1 x 0 = 0.5
t 2 = 18 x 2 = 0 Δ x 2 = x 2 x 1 = −0.5
t 3 = 33 x 3 = 1.0 Δ x 3 = x 3 x 2 = 1.0
t 4 = 58 x 4 = −0.75 Δ x 4 = x 4 x 3 = −1.75

Solution

  1. From the above table, the total displacement is
    Δ x i = 0.5 0.5 + 1.0 1.75 km = −0.75 km .
  2. The magnitude of the total displacement is | −0.75 | km = 0.75 km .
  3. Average velocity = Total displacement Elapsed time = v = −0.75 km 58 min = −0.013 km/min
  4. The total distance traveled (sum of magnitudes of individual displacements) is x Total = | Δ x i | = 0.5 + 0.5 + 1.0 + 1.75 km = 3.75 km .
  5. We can graph Jill’s position versus time as a useful aid to see the motion; the graph is shown in [link] .
    Graph shows position in kilometers plotted as a function of time in minutes.
    This graph depicts Jill’s position versus time. The average velocity is the slope of a line connecting the initial and final points.

Significance

Jill’s total displacement is −0.75 km, which means at the end of her trip she ends up 0.75 km due west of her home. The average velocity means if someone was to walk due west at 0.013 km/min starting at the same time Jill left her home, they both would arrive at the final stopping point at the same time. Note that if Jill were to end her trip at her house, her total displacement would be zero, as well as her average velocity. The total distance traveled during the 58 minutes of elapsed time for her trip is 3.75 km.

Check Your Understanding A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is his displacement? (b) What is the distance traveled? (c) What is the magnitude of his displacement?

Figure shows timeline of cyclist’s movement. First displacement is to the left by 3.0 kilometers. Second displacement is from the final point to the right by 2.0 kilometers.

(a) The rider’s displacement is Δ x = x f x 0 = −1 km . (The displacement is negative because we take east to be positive and west to be negative.) (b) The distance traveled is 3 km + 2 km = 5 km. (c) The magnitude of the displacement is 1 km.

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Summary

  • Kinematics is the description of motion without considering its causes. In this chapter, it is limited to motion along a straight line, called one-dimensional motion.
  • Displacement is the change in position of an object. The SI unit for displacement is the meter. Displacement has direction as well as magnitude.
  • Distance traveled is the total length of the path traveled between two positions.
  • Time is measured in terms of change. The time between two position points x 1 and x 2 is Δ t = t 2 t 1 . Elapsed time for an event is Δ t = t f t 0 , where t f is the final time and t 0 is the initial time. The initial time is often taken to be zero.
  • Average velocity v is defined as displacement divided by elapsed time. If x 1 , t 1 and x 2 , t 2 are two position time points, the average velocity between these points is
    v = Δ x Δ t = x 2 x 1 t 2 t 1 .

Conceptual questions

Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Identify each quantity in your example specifically.

You drive your car into town and return to drive past your house to a friend’s house.

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Under what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and displacement are exactly the same?

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Bacteria move back and forth using their flagella (structures that look like little tails). Speeds of up to 50 μm/s (50 × 10 −6 m/s) have been observed. The total distance traveled by a bacterium is large for its size, whereas its displacement is small. Why is this?

If the bacteria are moving back and forth, then the displacements are canceling each other and the final displacement is small.

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Give an example of a device used to measure time and identify what change in that device indicates a change in time.

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Does a car’s odometer measure distance traveled or displacement?

Distance traveled

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During a given time interval the average velocity of an object is zero. What can you say conclude about its displacement over the time interval?

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Problems

Consider a coordinate system in which the positive x axis is directed upward vertically. What are the positions of a particle (a) 5.0 m directly above the origin and (b) 2.0 m below the origin?

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A car is 2.0 km west of a traffic light at t = 0 and 5.0 km east of the light at t = 6.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) What are the car’s position vectors at these two times? (b) What is the car’s displacement between 0 min and 6.0 min?

a. x 1 = ( −2.0 m ) i ^ , x 2 = ( 5.0 m ) i ^ ; b. 7.0 m east

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The Shanghai maglev train connects Longyang Road to Pudong International Airport, a distance of 30 km. The journey takes 8 minutes on average. What is the maglev train’s average velocity?

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The position of a particle moving along the x -axis is given by x ( t ) = 4.0 2.0 t m. (a) At what time does the particle cross the origin? (b) What is the displacement of the particle between t = 3.0 s and t = 6.0 s ?

a. t = 2.0 s; b. x ( 6.0 ) x ( 3.0 ) = −8.0 ( −2.0 ) = −6.0 m

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A cyclist rides 8.0 km east for 20 minutes, then he turns and heads west for 8 minutes and 3.2 km. Finally, he rides east for 16 km, which takes 40 minutes. (a) What is the final displacement of the cyclist? (b) What is his average velocity?

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On February 15, 2013, a superbolide meteor (brighter than the Sun) entered Earth’s atmosphere over Chelyabinsk, Russia, and exploded at an altitude of 23.5 km. Eyewitnesses could feel the intense heat from the fireball, and the blast wave from the explosion blew out windows in buildings. The blast wave took approximately 2 minutes 30 seconds to reach ground level. (a) What was the average velocity of the blast wave? b) Compare this with the speed of sound, which is 343 m/s at sea level.

a. 150.0 s, v = 156.7 m/s ; b. 45.7% the speed of sound at sea level

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Questions & Answers

Can someone please tell what really happened to planet Pluto
Ejiba Reply
what are the first 20 elements in periodic table.
Ejiba Reply
H,O...
Arzoodan
what happened to the rest now, or have you forgotten?
Ejiba
who discover periodic table?
lovet Reply
it wasn't discovered , it was made.and the person who made it was dmitri mendeleev. dobreinier and newland gave their laws before dmitri related periodic table but wasn't successful in their work
Ritik
Nope, numerous number of scientist had actually contributed in the making of periodic table. Dmitri Mendeleev succeeded making all the elements into the right order in accordance to their atomic number.
Dame
what is the Greek name for calcium
Oniyide Reply
Greek word for calcium is asvestio while Latin name is calf meaning lime or limestone
Ejiba
different types of wave
Yog Reply
longitudinal and transverse waves
Ravindra
a gun is kept in the state that it cannot move anywhere and the bullet is fired. Then what is the effect on the velocity of bullet and KE of gun ?
Gobinda Reply
want is meant by the term solar system
jafar Reply
it refers to the sun and all heavenly bodies revolving around it.
Danie
excatly...for sure
Arzoodan
in addition to Danie's, a solar system is a collection of planets and their moons, asteroids, and other objects bound together by the Star's gravitational force directly or indirectly.
Galiwango
what is meant by total internal reflection
Akshay Reply
what iw meant by total internal reflection
Akshay
Lorentz force?
jyotirmayee
study fibre optics. .you will get total internal reflection
Siddhansh
wha
jyotirmayee
what is Lorentz force?
jyotirmayee
a ray of light traveling at an angle of incidence greater than critical angle from denser to rarer medium is totally reflected back into the denser medium is called total internal reflaction
Manoj
motion in strat line where is this chapter
Vijaybhai Reply
motion in straight line is kinematic's part
Ritik
yea
Manoj
this defination isn't correct
Arzoodan
motion in one dimension
Anil
what is Lorentz force?
jyotirmayee Reply
what is maxwell electromagnetic law?
jyotirmayee
at what angle should the two forces 2p and root 2p acts so that the resultant force is p root 10
Akshay Reply
what answer fir this
Akshay
what's the working difference between a dynamo and a pump?
Piyali Reply
a dynamo is basically a dc generator while pump is usually equipped with a motor
vedanth
a dynamo converts mechanical energy to electrical while a pump is opposite to that
vedanth
nice
Piyali
okay
Friday
why sea water looks bluish?
Piyali Reply
cuz the sky is blue...
Mehdi
you see the reflexion of the "blue" sky in the water
Mehdi
somewhere sea water turns green why?
Piyali
never seen bro... are u sure ?
Mehdi
ur answer was correct but due to the presence of phytoplankton color can be changed near the shore
Piyali
waaaww... you re awesome
Mehdi
because of the reflection of the sky
Friday
rays coming from the sun consist of all 7 colours ie.VIBGYOR. when the ray strikes surface of water,all colors gets absorbed by it except blue which gets reflected by it.so we find the sea water appearing bluish
Ritik
how can someone identify sea water from rain water
Oniyide
i think it's not possible as because rainwater consists of water from all kind of water bodies ie.lakes,seas etc but u can predict if u have a sea nearby ur home or city
Ritik
i need solutions of unuversity pbysucs volume 1
Vimla Reply
me too
Nirupam
Help us if anyone knows
Nirupam
bring questions
john
actually if u wanted whole book solution then u should buy the solution book
jyotirmayee
from where
Nirupam
where do u live ,,,,,if u live in Delhi then at bellsarayeiii or from stationary store ,,,,chatarpurrr ,,,,,there is a popular books store,,,,,u have to buy from there
jyotirmayee
Kota Rajasthan
Nirupam
so strange,,,,,r u preparing for pmt,,,?
jyotirmayee
for IIT
Nirupam
then concern near book store
jyotirmayee
in Rajasthan
jyotirmayee
or ask questions here
jyotirmayee
thanks for your help
Nirupam
its fine,,most welcome
jyotirmayee
what is three dimensional coordinate system?
Sachindra Reply
considering the change of vectors in all three dimensions of space
vedanth
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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