<< Chapter < Page | Chapter >> Page > |
A sketch of Jill’s movements is shown in [link] .
Time t _{i} (min) | Position ${x}_{i}$ (km) | Displacement $\text{\Delta}{x}_{\text{i}}$ (km) |
---|---|---|
${t}_{0}=0$ | ${x}_{0}=0$ | $\text{\Delta}{x}_{0}=0$ |
${t}_{1}=9$ | ${x}_{1}=0.5$ | $\text{\Delta}{x}_{1}={x}_{1}-{x}_{0}=0.5$ |
${t}_{2}=18$ | ${x}_{2}=0$ | $\text{\Delta}{x}_{2}={x}_{2}-{x}_{1}=\mathrm{-0.5}$ |
${t}_{3}=33$ | ${x}_{3}=1.0$ | $\text{\Delta}{x}_{3}={x}_{3}-{x}_{2}=1.0$ |
${t}_{4}=58$ | ${x}_{4}=\mathrm{-0.75}$ | $\text{\Delta}{x}_{4}={x}_{4}-{x}_{3}=\mathrm{-1.75}$ |
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?
(a) The rider’s displacement is $\text{\Delta}x={x}_{\text{f}}-{x}_{0}=\mathrm{-1}\phantom{\rule{0.2em}{0ex}}\text{km}$ . (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.
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.
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?
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.
Give an example of a device used to measure time and identify what change in that device indicates a change in time.
Does a car’s odometer measure distance traveled or displacement?
Distance traveled
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?
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?
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. ${\overrightarrow{x}}_{1}=(\mathrm{-2.0}\phantom{\rule{0.2em}{0ex}}\text{m})\widehat{i}$ , ${\overrightarrow{x}}_{2}=(5.0\phantom{\rule{0.2em}{0ex}}\text{m})\widehat{i}$ ; b. 7.0 m east
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?
The position of a particle moving along the x -axis is given by $x(t)=4.0-2.0t$ m. (a) At what time does the particle cross the origin? (b) What is the displacement of the particle between $\text{t}=3.0\phantom{\rule{0.2em}{0ex}}\text{s}$ and $\text{t}=6.0\phantom{\rule{0.2em}{0ex}}\text{s}?$
a. $t=2.0$ s; b. $x(6.0)-x(3.0)=\mathrm{-8.0}-(\mathrm{-2.0})=\mathrm{-6.0}\phantom{\rule{0.2em}{0ex}}\text{m}$
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?
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, $\stackrel{\text{\u2013}}{v}=156.7\phantom{\rule{0.2em}{0ex}}\text{m/s}$ ; b. 45.7% the speed of sound at sea level
Notification Switch
Would you like to follow the 'University physics volume 1' conversation and receive update notifications?