<< Chapter < Page Chapter >> Page >
  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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Distance traveled

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
Daniel Reply
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
One answer for that is exchange particles. Those particlescreate a field and if there is a field e.g. electromagnetic there is also force. same should go for gravitational field where exchange particle is called graviton and it creates gravitational field, which acts on everything that has mass.
Resid
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
Goodness Reply
what is the formula for pressure?
Goodness Reply
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
John Reply
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
Daniel
and the color spectrum
Daniel
what is a scalar quantity
Peter Reply
scalar: are quantity have numerical value
muslim
is that a better way in defining scalar quantity
Peter
thanks
muslim
quantity that has magnitude but no direction
Peter
upward force and downward force lift
adegboye Reply
upward force and downward force on lift
adegboye
hi
Etini
hi
elo
hy
Xander
Hello
Jux_dob
hi
Peter
Helo
Tobi
Yes what about it?
Daniel
what's the answer? I can't get it
Rachel Reply
what is the question again?
Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
How many kilometres in 1 mile
Nessy
1.609km in 1mile
Faqir
what's the si unit of impulse
Iguh Reply
The Newton second (N•s)
Ethan
what is the s. I unit of current
Roland Reply
Amphere(A)
imam
thanks man
Roland
u r welcome
imam
the velocity of a boat related to water is 3i+4j and that of water related to earth is i-3j. what is the velocity of the boat relative to earth.If unit vector i and j represent 1km/hour east and north respectively
Pallavi Reply
what is head to tail rule?
kinza Reply
Explain Head to tail rule?
kinza
what is the guess theorem
Monu Reply
viva question and answer on practical youngs modulus by streching
Akash Reply
send me vvi que
rupesh
a car can cover a distance of 522km on 36 Liter's of petrol, how far can it travel on 14 liter of petrol.
Isaac
yoo the ans is 193
Joseph
whats a two dimensional force
Jimoh Reply
what are two dimensional force?
Ahmad
Where is Fourier Theorem?
Atul Reply
Practice Key Terms 7

Get the best University physics vol... course in your pocket!





Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 1' conversation and receive update notifications?

Ask