An Object Is Traveling at 20m/sec to the Left. What Is It's Speed and Velocity

Department Learning Objectives

Past the end of this section, you will be able to do the post-obit:

• Calculate the average speed of an object
• Relate displacement and average velocity

Teacher Support

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
  • (B) describe and analyze motion in ane dimension using equations with the concepts of distance, displacement, speed, average velocity, instantaneous velocity, and acceleration.

In addition, the High School Physics Laboratory Transmission addresses content in this section in the lab titled: Position and Speed of an Object, equally well as the following standards:

• (four) Scientific discipline concepts. The student knows and applies the laws governing motion in a variety of situations. The educatee is expected to:
  • (B) depict and analyze motion in one dimension using equations with the concepts of distance, displacement, speed, boilerplate velocity, instantaneous velocity, and acceleration.

Department Cardinal Terms

boilerplate speed	average velocity	instantaneous speed
instantaneous velocity	speed	velocity

Instructor Support

Instructor Support

In this section, students will apply what they have learned about distance and displacement to the concepts of speed and velocity.

[BL] [OL] Before students read the section, ask them to give examples of ways they have heard the word speed used. Then ask them if they have heard the word velocity used. Explain that these words are oft used interchangeably in everyday life, but their scientific definitions are different. Tell students that they volition learn nigh these differences as they read the section.

[AL] Explicate to students that velocity, like displacement, is a vector quantity. Enquire them to speculate about means that speed is different from velocity. After they share their ideas, follow upwardly with questions that deepen their thought process, such every bit: Why practise y'all call up that? What is an instance? How might apply these terms to motion that you see every day?

Speed

There is more to motion than distance and deportation. Questions such as, "How long does a foot race take?" and "What was the runner's speed?" cannot be answered without an understanding of other concepts. In this department we will look at time, speed, and velocity to aggrandize our agreement of motion.

A clarification of how fast or wearisome an object moves is its speed. Speed is the charge per unit at which an object changes its location. Like distance, speed is a scalar considering it has a magnitude but not a direction. Because speed is a charge per unit, it depends on the time interval of motion. You can calculate the elapsed fourth dimension or the alter in time, $\Delta t$ , of motion as the difference between the ending time and the beginning time

$$\Delta t=t_{\text{f}}-t_{\text{0}}.$$

The SI unit of time is the 2nd (s), and the SI unit of speed is meters per second (one thousand/s), but sometimes kilometers per hour (km/h), miles per hour (mph) or other units of speed are used.

When yous describe an object'due south speed, you ofttimes describe the average over a time period. Average speed, v _avg , is the altitude traveled divided by the time during which the motion occurs.

$${\mathrm{five}}_{\text{avg}}=\frac{\text{distance}}{\text{time}}$$

You can, of class, rearrange the equation to solve for either distance or time

$$\text{fourth dimension =}\frac{\text{altitude}}{v_{\text{avg}}}\text{.}$$

$$\text{distance =}{\mathrm{five}}_{\text{avg}}\text{ × time}$$

Suppose, for case, a car travels 150 kilometers in 3.two hours. Its average speed for the trip is

$$\begin{array}{ccc}\hfill v_{\text{avg}}& =& \frac{\text{distance}}{\text{time}}\hfill \\ & =& \frac{150\text{ km}}{\mathrm{3.ii}\text{ h}}\hfill \\ & =& 47\text{ km/h.}\hfill \end{array}$$

A machine'southward speed would probable increase and decrease many times over a 3.ii hr trip. Its speed at a specific instant in time, however, is its instantaneous speed. A machine's speedometer describes its instantaneous speed.

Teacher Support

Teacher Support

[OL] [AL] Circumspection students that average speed is not always the average of an object's initial and final speeds. For example, suppose a car travels a altitude of 100 km. The outset 50 km it travels xxx km/h and the second 50 km information technology travels at lx km/h. Its boilerplate speed would be distance /(fourth dimension interval) = (100 km)/[(50 km)/(30 km/h) + (50 km)/(60 km/h)] = xl km/h. If the car had spent equal times at 30 km and threescore km rather than equal distances at these speeds, its boilerplate speed would have been 45 km/h.

[BL] [OL] Caution students that the terms speed, average speed, and instantaneous speed are all often referred to simply as speed in everyday language. Emphasize the importance in science to use correct terminology to avoid confusion and to properly communicate ideas.

Effigy 2.8 During a 30-minute round trip to the store, the total distance traveled is 6 km. The boilerplate speed is 12 km/h. The deportation for the round trip is zero, because there was no cyberspace change in position.

Worked Case

Calculating Average Speed

A marble rolls five.2 m in 1.8 due south. What was the marble's boilerplate speed?

Strategy

Nosotros know the distance the marble travels, v.ii 1000, and the fourth dimension interval, 1.viii southward. Nosotros can use these values in the average speed equation.

Discussion

Average speed is a scalar, and then we exercise not include management in the reply. Nosotros can check the reasonableness of the respond by estimating: 5 meters divided by ii seconds is 2.v m/s. Since ii.5 m/s is shut to two.9 chiliad/s, the answer is reasonable. This is about the speed of a brisk walk, so it also makes sense.

Do Issues

9 .

A pitcher throws a baseball from the pitcher's mound to dwelling plate in 0.46 s. The distance is 18.4 g. What was the average speed of the baseball?

1. 40 m/s
2. - twoscore 1000/s
3. 0.03 yard/s
4. 8.5 one thousand/s

10 .

Cassie walked to her friend's house with an average speed of 1.40 m/s. The altitude between the houses is 205 yard. How long did the trip take her?

1. 146 s

2. 0.01 s

3. 2.fifty min

4. 287 s

Velocity

The vector version of speed is velocity. Velocity describes the speed and direction of an object. As with speed, it is useful to describe either the average velocity over a time period or the velocity at a specific moment. Boilerplate velocity is displacement divided by the time over which the displacement occurs.

$${\mathrm{five}}_{\text{avg}}=\frac{\text{displacement}}{\text{time}}=\frac{\Delta d}{\Delta t}=\frac{d_{\text{f}}-d_0}{t_{\text{f}}-t_0}$$

Velocity, like speed, has SI units of meters per second (m/s), just considering it is a vector, you lot must likewise include a direction. Furthermore, the variable v for velocity is bold because information technology is a vector, which is in contrast to the variable 5 for speed which is italicized considering information technology is a scalar quantity.

Tips For Success

It is important to go along in heed that the boilerplate speed is not the same affair as the average velocity without its direction. Like we saw with displacement and distance in the concluding section, changes in direction over a time interval have a bigger outcome on speed and velocity.

Suppose a rider moved toward the back of a plane with an boilerplate velocity of –four m/s. Nosotros cannot tell from the boilerplate velocity whether the passenger stopped momentarily or backed up before he got to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals such equally those shown in Figure ii.9. If you consider infinitesimally small intervals, you tin can define instantaneous velocity, which is the velocity at a specific instant in time. Instantaneous velocity and boilerplate velocity are the aforementioned if the velocity is constant.

Effigy two.ix The diagram shows a more detailed record of an airplane passenger heading toward the back of the plane, showing smaller segments of his trip.

Earlier, y'all have read that altitude traveled can be unlike than the magnitude of deportation. In the aforementioned style, speed can be different than the magnitude of velocity. For example, you drive to a shop and return home in half an hour. If your car'due south odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your boilerplate velocity, however, was zippo because your displacement for the round trip is zilch.

Lookout man Physics

Computing Boilerplate Velocity or Speed

This video reviews vectors and scalars and describes how to summate boilerplate velocity and average speed when you lot know displacement and change in time. The video likewise reviews how to convert km/h to thousand/s.

Which of the following fully describes a vector and a scalar quantity and correctly provides an instance of each?

1. A scalar quantity is fully described past its magnitude, while a vector needs both magnitude and direction to fully draw it. Deportation is an example of a scalar quantity and time is an example of a vector quantity.

2. A scalar quantity is fully described past its magnitude, while a vector needs both magnitude and management to fully depict it. Time is an case of a scalar quantity and displacement is an case of a vector quantity.

3. A scalar quantity is fully described by its magnitude and direction, while a vector needs only magnitude to fully draw it. Deportation is an example of a scalar quantity and time is an example of a vector quantity.

4. A scalar quantity is fully described by its magnitude and direction, while a vector needs only magnitude to fully describe it. Time is an instance of a scalar quantity and displacement is an case of a vector quantity.

Teacher Back up

Teacher Support

This video does a good task of reinforcing the difference between vectors and scalars. The educatee is introduced to the idea of using 's' to denote displacement, which you lot may or may non wish to encourage. Earlier students spotter the video, point out that the instructor uses $\overrightarrow{s}$ for deportation instead of d, as used in this text. Explain the use of small arrows over variables is a common style to denote vectors in higher-level physics courses. Caution students that the customary abbreviations for hr and seconds are non used in this video. Remind students that in their own work they should employ the abbreviations h for hour and s for seconds.

Worked Example

Computing Boilerplate Velocity

A pupil has a displacement of 304 m north in 180 due south. What was the student's boilerplate velocity?

Strategy

Nosotros know that the displacement is 304 m north and the time is 180 southward. We tin utilise the formula for average velocity to solve the problem.

Discussion

Since average velocity is a vector quantity, you must include direction every bit well every bit magnitude in the answer. Notice, however, that the direction can be omitted until the end to avoid cluttering the problem. Pay attention to the significant figures in the trouble. The distance 304 m has 3 significant figures, but the fourth dimension interval 180 s has only two, then the caliber should have simply ii pregnant figures.

Tips For Success

Note the way scalars and vectors are represented. In this book d represents distance and displacement. Similarly, 5 represents speed, and v represents velocity. A variable that is not bold indicates a scalar quantity, and a bold variable indicates a vector quantity. Vectors are sometimes represented past small arrows to a higher place the variable.

Instructor Support

Instructor Back up

Use this problem to emphasize the importance of using the right number of significant figures in calculations. Some students accept a tendency to include many digits in their terminal calculations. They incorrectly believe they are improving the accuracy of their answer by writing many of the digits shown on the calculator. Point out that doing this introduces errors into the calculations. In more complicated calculations, these errors tin propagate and crusade the terminal answer to exist wrong. Instead, remind students to always carry ane or two extra digits in intermediate calculations and to circular the final answer to the right number of pregnant figures.

Worked Example

Solving for Displacement when Average Velocity and Time are Known

Layla jogs with an boilerplate velocity of 2.iv m/s east. What is her displacement after 46 seconds?

Strategy

We know that Layla's average velocity is 2.4 m/due south east, and the fourth dimension interval is 46 seconds. Nosotros tin can rearrange the average velocity formula to solve for the displacement.

Give-and-take

The reply is about 110 thou east, which is a reasonable deportation for slightly less than a minute of jogging. A computer shows the answer as 110.four g. Nosotros chose to write the answer using scientific notation because we wanted to get in clear that nosotros merely used two significant figures.

Tips For Success

Dimensional assay is a good mode to make up one's mind whether y'all solved a problem correctly. Write the calculation using merely units to exist sure they match on opposite sides of the equal marker. In the worked example, you have
m = (m/south)(s). Since seconds is in the denominator for the average velocity and in the numerator for the time, the unit cancels out leaving only thou and, of course, yard = m.

Worked Example

Solving for Time when Displacement and Boilerplate Velocity are Known

Phillip walks forth a directly path from his house to his school. How long volition it have him to become to school if he walks 428 m west with an boilerplate velocity of one.vii g/south west?

Strategy

We know that Phillip's displacement is 428 chiliad west, and his average velocity is ane.seven m/s westward. We can calculate the time required for the trip by rearranging the boilerplate velocity equation.

Discussion

Here again we had to apply scientific note because the answer could simply have 2 significant figures. Since time is a scalar, the reply includes only a magnitude and not a management.

Exercise Problems

11 .

A trucker drives along a straight highway for 0.25 h with a displacement of sixteen km due south. What is the trucker's average velocity?

1. 4 km/h north

2. 4 km/h south

3. 64 km/h north

4. 64 km/h south

12 .

A bird flies with an boilerplate velocity of 7.5 yard/s eastward from one branch to some other in 2.4 southward. It then pauses earlier flight with an average velocity of six.8 m/s east for 3.v south to another branch. What is the bird'due south total displacement from its starting point?

1. 42 m west
2. vi m west
3. six 1000 e
4. 42 m due east

Virtual Physics

The Walking Man

In this simulation you will put your cursor on the man and motility him outset in ane direction and so in the reverse management. Keep the Introduction tab active. You can use the Charts tab after you acquire nearly graphing movement afterwards in this chapter. Carefully lookout the sign of the numbers in the position and velocity boxes. Ignore the acceleration box for now. Come across if you can make the man's position positive while the velocity is negative. Then see if y'all tin do the contrary.

Grasp Check

Which situation correctly describes when the moving man's position was negative but his velocity was positive?

1. Homo moving toward 0 from left of 0
2. Homo moving toward 0 from correct of 0
3. Homo moving away from 0 from left of 0
4. Man moving away from 0 from correct of 0

Teacher Support

Teacher Back up

This is a powerful interactive animation, and it can exist used for many lessons. At this point it can be used to bear witness that deportation can be either positive or negative. Information technology can also prove that when displacement is negative, velocity tin be either positive or negative. Later it can be used to show that velocity and acceleration can have different signs. It is strongly suggested that you go along students on the Introduction tab. The Charts tab tin can be used after students larn almost graphing motion afterwards in this chapter.

Bank check Your Agreement

13 .

Two runners traveling forth the same straight path start and finish their run at the same time. At the halfway mark, they have dissimilar instantaneous velocities. Is it possible for their average velocities for the unabridged trip to be the aforementioned?

1. Aye, because average velocity depends on the net or total deportation.

2. Yes, because average velocity depends on the total distance traveled.

3. No, considering the velocities of both runners must remain exactly the same throughout the journey.

4. No, because the instantaneous velocities of the runners must remain the same at the midpoint simply can vary at other points.

xiv .

If you carve up the total altitude traveled on a auto trip (as adamant by the odometer) by the time for the trip, are you computing the boilerplate speed or the magnitude of the average velocity, and under what circumstances are these two quantities the same?

1. Average speed. Both are the same when the car is traveling at a constant speed and changing direction.
2. Boilerplate speed. Both are the same when the speed is constant and the car does not change its direction.
3. Magnitude of average velocity. Both are aforementioned when the motorcar is traveling at a constant speed.
4. Magnitude of average velocity. Both are same when the machine does not change its management.

15 .

Is it possible for boilerplate velocity to be negative?

1. Yes, if internet displacement is negative.

2. Yes, if the object's direction changes during motion.

3. No, because average velocity describes but the magnitude and not the direction of motion.

4. No, considering boilerplate velocity only describes the magnitude in the positive direction of motion.

Teacher Support

Teacher Support

Use the Check Your Understanding questions to assess students' accomplishment of the sections learning objectives. If students are struggling with a specific objective, the Check Your Understanding will assistance identify which and direct students to the relevant content. Assessment items in TUTOR volition let you to reassess.

Share this post