A 70 Kg Bicyclist Rides His 98 Kg Bicycle With a Speed of 15 M/s You May Want to Review

Section Learning Objectives

By the end of this section, you will be able to do the following:

• Calculate the average speed of an object
• Chronicle displacement and boilerplate velocity

Teacher Support

Instructor Back up

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

• (iv) Science concepts. The pupil knows and applies the laws governing motion in a variety of situations. The educatee is expected to:
  • (B) describe and analyze motion in one 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 equally the post-obit standards:

• (iv) Science concepts. The student knows and applies the laws governing movement in a variety of situations. The educatee is expected to:
  • (B) describe and analyze motility in one dimension using equations with the concepts of altitude, deportation, speed, average velocity, instantaneous velocity, and acceleration.

Section Key Terms

average speed	average velocity	instantaneous speed
instantaneous velocity	speed	velocity

Teacher Back up

Teacher Support

In this section, students will utilise what they have learned nigh distance and deportation to the concepts of speed and velocity.

[BL] [OL] Before students read the section, ask them to give examples of means they have heard the word speed used. Then enquire them if they take heard the give-and-take velocity used. Explain that these words are often used interchangeably in everyday life, but their scientific definitions are different. Tell students that they will learn most these differences as they read the section.

[AL] Explicate to students that velocity, like displacement, is a vector quantity. Ask them to speculate virtually ways that speed is different from velocity. Later they share their ideas, follow up with questions that deepen their idea process, such every bit: Why practice you think that? What is an case? How might utilize these terms to motion that you lot run into every day?

Speed

There is more to move than altitude and displacement. Questions such as, "How long does a foot race take?" and "What was the runner's speed?" cannot exist answered without an agreement of other concepts. In this section nosotros volition look at time, speed, and velocity to expand our understanding of movement.

A description of how fast or deadening an object moves is its speed. Speed is the rate at which an object changes its location. Like distance, speed is a scalar because it has a magnitude only non a direction. Because speed is a rate, it depends on the time interval of motion. Y'all can calculate the elapsed time or the alter in time, $\Delta t$ , of motion as the divergence between the ending time and the first time

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

The SI unit of time is the second (southward), and the SI unit of speed is meters per second (chiliad/south), but sometimes kilometers per 60 minutes (km/h), miles per hr (mph) or other units of speed are used.

When you describe an object's speed, you oftentimes describe the average over a time period. Boilerplate speed, v _avg , is the distance traveled divided past the time during which the movement occurs.

$$5_{\text{avg}}=\frac{\text{distance}}{\text{fourth dimension}}$$

You can, of course, rearrange the equation to solve for either altitude or time

$$\text{time =}\frac{\text{distance}}{5_{\text{avg}}}\text{.}$$

$$\text{altitude =}{v}_{\text{avg}}\text{ × time}$$

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

$$\begin{array}{ccc}\hfill v_{\text{avg}}& =& \frac{\text{distance}}{\text{time}}\hfill \\ & =& \frac{150\text{ km}}{3.2\text{ h}}\hfill \\ & =& 47\text{ km/h.}\hfill \end{array}$$

A car's speed would probable increase and subtract many times over a 3.two hour trip. Its speed at a specific instant in time, however, is its instantaneous speed. A automobile'south speedometer describes its instantaneous speed.

Teacher Support

Teacher Back up

[OL] [AL] Caution students that average speed is non ever the average of an object's initial and terminal speeds. For example, suppose a car travels a altitude of 100 km. The first fifty km it travels 30 km/h and the second fifty km it travels at 60 km/h. Its average speed would be distance /(time interval) = (100 km)/[(l km)/(thirty km/h) + (fifty km)/(60 km/h)] = 40 km/h. If the car had spent equal times at 30 km and 60 km rather than equal distances at these speeds, its average speed would have been 45 km/h.

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

Effigy ii.eight During a 30-minute round trip to the shop, the total distance traveled is 6 km. The boilerplate speed is 12 km/h. The displacement for the round trip is zero, because in that location was no net change in position.

Worked Example

Calculating Average Speed

A marble rolls 5.2 m in 1.8 south. What was the marble's average speed?

Strategy

We know the altitude the marble travels, 5.two grand, and the time interval, one.viii s. We can use these values in the boilerplate speed equation.

Discussion

Average speed is a scalar, so we do not include direction in the answer. Nosotros can cheque the reasonableness of the answer past estimating: v meters divided by 2 seconds is two.5 m/s. Since two.5 m/southward is close to 2.9 m/southward, the answer is reasonable. This is almost the speed of a brisk walk, so it likewise makes sense.

Practice Issues

9 .

A bullpen throws a baseball from the pitcher'southward mound to home plate in 0.46 s. The distance is eighteen.4 k. What was the boilerplate speed of the baseball?

1. 40 m/s
2. - 40 m/southward
3. 0.03 chiliad/southward
4. 8.5 m/s

ten .

Cassie walked to her friend's business firm with an average speed of i.40 m/s. The distance betwixt the houses is 205 m. How long did the trip have her?

1. 146 s

2. 0.01 s

3. 2.50 min

4. 287 s

Velocity

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

$$v_{\text{avg}}=\frac{\text{displacement}}{\text{fourth dimension}}=\frac{\Delta d}{\Delta t}=\frac{d_{\text{f}}-d_0}{t_{\text{f}}-t_0}$$

Velocity, similar speed, has SI units of meters per 2nd (thousand/southward), but because it is a vector, yous must also include a management. Furthermore, the variable v for velocity is assuming because it is a vector, which is in dissimilarity to the variable v for speed which is italicized because it is a scalar quantity.

Tips For Success

It is of import to go on in mind that the average speed is not the aforementioned thing as the average velocity without its direction. Like nosotros saw with displacement and distance in the last section, changes in direction over a time interval have a bigger consequence on speed and velocity.

Suppose a passenger moved toward the back of a plane with an average velocity of –4 m/s. We cannot tell from the average velocity whether the rider stopped momentarily or backed up before he got to the back of the plane. To become more details, we must consider smaller segments of the trip over smaller fourth dimension intervals such as those shown in Figure 2.9. If yous consider infinitesimally small intervals, you tin can define instantaneous velocity, which is the velocity at a specific instant in time. Instantaneous velocity and average velocity are the aforementioned if the velocity is constant.

Figure 2.nine The diagram shows a more than detailed record of an airplane passenger heading toward the back of the plane, showing smaller segments of his trip.

Earlier, you have read that distance traveled can exist different than the magnitude of deportation. In the aforementioned way, speed tin be dissimilar than the magnitude of velocity. For example, you drive to a store and return abode in half an hr. If your machine's odometer shows the total altitude traveled was 6 km, and so your average speed was 12 km/h. Your average velocity, however, was goose egg considering your displacement for the circular trip is aught.

Watch Physics

Calculating Boilerplate Velocity or Speed

This video reviews vectors and scalars and describes how to calculate average velocity and average speed when you know displacement and change in fourth dimension. The video as well reviews how to catechumen km/h to grand/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 by its magnitude, while a vector needs both magnitude and direction to fully draw it. Displacement is an case of a scalar quantity and time is an case 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 information technology. Time is an instance 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 merely magnitude to fully describe it. Displacement is an case of a scalar quantity and time is an example of a vector quantity.

4. A scalar quantity is fully described by its magnitude and management, while a vector needs merely magnitude to fully depict information technology. Time is an example of a scalar quantity and displacement is an example of a vector quantity.

Teacher Back up

Teacher Back up

This video does a good chore of reinforcing the difference between vectors and scalars. The student is introduced to the idea of using 'southward' to announce displacement, which you may or may not wish to encourage. Earlier students watch the video, bespeak out that the teacher uses $\overrightarrow{s}$ for displacement instead of d, as used in this text. Explain the use of minor arrows over variables is a common way to announce vectors in higher-level physics courses. Caution students that the customary abbreviations for hour and seconds are not used in this video. Remind students that in their own work they should apply the abbreviations h for hour and due south for seconds.

Worked Example

Calculating Average Velocity

A student has a displacement of 304 k north in 180 s. What was the student'south average velocity?

Strategy

We know that the displacement is 304 m north and the time is 180 southward. We can use the formula for boilerplate velocity to solve the problem.

Give-and-take

Since boilerplate velocity is a vector quantity, you must include direction as well equally magnitude in the answer. Notice, nonetheless, that the management can be omitted until the finish to avert cluttering the problem. Pay attention to the significant figures in the problem. The distance 304 chiliad has three significant figures, just the time interval 180 southward has only two, so the quotient should take only two significant figures.

Tips For Success

Note the style scalars and vectors are represented. In this book d represents distance and deportation. Similarly, v represents speed, and v represents velocity. A variable that is non bold indicates a scalar quantity, and a bold variable indicates a vector quantity. Vectors are sometimes represented by small arrows above the variable.

Teacher Back up

Teacher Back up

Employ this problem to emphasize the importance of using the correct number of significant figures in calculations. Some students have a tendency to include many digits in their final calculations. They incorrectly believe they are improving the accurateness 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 than complicated calculations, these errors can propagate and cause the final answer to exist wrong. Instead, remind students to always carry 1 or two extra digits in intermediate calculations and to round the final reply to the correct number of pregnant figures.

Worked Case

Solving for Deportation when Average Velocity and Fourth dimension are Known

Layla jogs with an average velocity of 2.4 m/s east. What is her displacement later 46 seconds?

Strategy

We know that Layla's average velocity is 2.iv thousand/southward eastward, and the time interval is 46 seconds. We can rearrange the average velocity formula to solve for the displacement.

Give-and-take

The answer is about 110 thou east, which is a reasonable deportation for slightly less than a infinitesimal of jogging. A calculator shows the answer every bit 110.iv m. We chose to write the answer using scientific notation because nosotros wanted to make it clear that we merely used two significant figures.

Tips For Success

Dimensional analysis is a good way to determine whether you solved a problem correctly. Write the calculation using only units to be sure they match on opposite sides of the equal mark. In the worked instance, you have
m = (m/s)(s). Since seconds is in the denominator for the average velocity and in the numerator for the time, the unit cancels out leaving only g and, of grade, m = m.

Worked Case

Solving for Fourth dimension when Displacement and Average Velocity are Known

Phillip walks along a direct path from his house to his school. How long will it take him to become to school if he walks 428 m due west with an average velocity of 1.7 grand/s westward?

Strategy

We know that Phillip's displacement is 428 m westward, and his average velocity is ane.7 yard/due south westward. Nosotros can calculate the time required for the trip by rearranging the boilerplate velocity equation.

Discussion

Here again we had to use scientific notation because the answer could just have 2 significant figures. Since time is a scalar, the answer includes only a magnitude and not a direction.

Practice Problems

11 .

A trucker drives along a direct highway for 0.25 h with a deportation of xvi km south. What is the trucker's average velocity?

1. iv km/h n

2. 4 km/h south

3. 64 km/h n

4. 64 km/h southward

12 .

A bird flies with an average velocity of 7.5 m/due south east from one branch to some other in 2.4 s. It then pauses before flying with an average velocity of 6.viii m/southward east for 3.five due south to some other branch. What is the bird's total displacement from its starting betoken?

1. 42 thousand west
2. 6 m west
3. 6 m east
4. 42 m east

Virtual Physics

The Walking Homo

In this simulation you will put your cursor on the man and move him first in one direction and so in the opposite management. Proceed the Introduction tab active. You can use the Charts tab after you learn almost graphing motion afterwards in this chapter. Carefully sentinel the sign of the numbers in the position and velocity boxes. Ignore the acceleration box for now. See if yous tin brand the homo'south position positive while the velocity is negative. Then see if you can do the opposite.

Grasp Cheque

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

1. Human being moving toward 0 from left of 0
2. Man moving toward 0 from correct of 0
3. Man moving abroad from 0 from left of 0
4. Homo moving away from 0 from right of 0

Teacher Support

Teacher Support

This is a powerful interactive animation, and information technology can be used for many lessons. At this point information technology can exist used to bear witness that displacement tin be either positive or negative. Information technology tin also testify that when deportation is negative, velocity tin be either positive or negative. Later it can be used to show that velocity and acceleration can have dissimilar signs. Information technology is strongly suggested that you keep students on the Introduction tab. The Charts tab can be used afterwards students larn about graphing motility later in this chapter.

Check Your Understanding

13 .

Two runners traveling along the aforementioned direct path kickoff and end their run at the same fourth dimension. At the halfway mark, they have different instantaneous velocities. Is information technology possible for their average velocities for the entire trip to be the aforementioned?

1. Yes, because average velocity depends on the net or total displacement.

2. Yeah, considering average velocity depends on the full altitude traveled.

3. No, because the velocities of both runners must remain exactly the same throughout the journeying.

4. No, considering the instantaneous velocities of the runners must remain the same at the midpoint but tin vary at other points.

14 .

If you divide the total distance traveled on a automobile trip (as adamant past the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the boilerplate velocity, and under what circumstances are these two quantities the same?

1. Average speed. Both are the same when the auto is traveling at a constant speed and changing management.
2. Average speed. Both are the same when the speed is constant and the car does non alter its management.
3. Magnitude of average velocity. Both are same when the car is traveling at a constant speed.
4. Magnitude of boilerplate velocity. Both are aforementioned when the automobile does not change its direction.

15 .

Is information technology possible for average velocity to exist negative?

1. Yes, if net displacement is negative.

2. Yes, if the object'south direction changes during move.

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

4. No, because average velocity simply describes the magnitude in the positive direction of move.

Teacher Back up

Instructor Back up

Apply the Check Your Understanding questions to assess students' achievement of the sections learning objectives. If students are struggling with a specific objective, the Check Your Understanding volition help identify which and direct students to the relevant content. Assessment items in TUTOR volition permit you to reassess.

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Source: https://openstax.org/books/physics/pages/2-2-speed-and-velocity

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