car goes from 40 m/s to 60m/s what is the average speed

Section Learning Objectives

By the stop of this section, you volition exist able to do the following:

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

Teacher Support

Teacher Back up

The learning objectives in this section volition help your students primary the post-obit standards:

• (four) Science concepts. The student knows and applies the laws governing motion in a multifariousness of situations. The pupil is expected to:
  • (B) depict and analyze motility in 1 dimension using equations with the concepts of distance, displacement, speed, average velocity, instantaneous velocity, and dispatch.

In improver, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Position and Speed of an Object, as well every bit the post-obit standards:

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

Section Key Terms

average speed	average velocity	instantaneous speed
instantaneous velocity	speed	velocity

Teacher 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 department, enquire them to give examples of ways they accept heard the word speed used. Then ask them if they have heard the give-and-take velocity used. Explain that these words are oft used interchangeably in everyday life, simply their scientific definitions are different. Tell students that they volition learn most these differences as they read the section.

[AL] Explain to students that velocity, like displacement, is a vector quantity. Ask them to speculate almost ways that speed is different from velocity. Later they share their ideas, follow up with questions that deepen their thought process, such equally: Why do you call back that? What is an instance? How might apply these terms to movement that you encounter every twenty-four hours?

Speed

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

A description of how fast or wearisome an object moves is its speed. Speed is the charge per unit at which an object changes its location. Similar distance, speed is a scalar because it has a magnitude merely not a direction. Because speed is a rate, it depends on the time interval of move. You tin calculate the elapsed time or the modify in fourth dimension, $\Delta t$ , of motion as the difference betwixt the ending time and the start time

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

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

When you draw an object's speed, you often describe the average over a fourth dimension period. Average speed, v _avg , is the distance traveled divided by the time during which the movement occurs.

$$v_{\text{avg}}=\frac{\text{distance}}{\text{time}}$$

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

$$\text{time =}\frac{\text{distance}}{v_{\text{avg}}}\text{.}$$

$$\text{distance =}{v}_{\text{avg}}\text{ × fourth dimension}$$

Suppose, for example, a automobile travels 150 kilometers in three.2 hours. Its average speed for the trip is

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

A car's speed would likely increase and subtract many times over a iii.two 60 minutes trip. Its speed at a specific instant in fourth dimension, however, is its instantaneous speed. A car's speedometer describes its instantaneous speed.

Teacher Support

Instructor Support

[OL] [AL] Circumspection students that average speed is not ever the average of an object'due south initial and final speeds. For instance, suppose a automobile travels a distance of 100 km. The showtime 50 km it travels 30 km/h and the 2d 50 km information technology travels at lx km/h. Its average speed would be distance /(time interval) = (100 km)/[(50 km)/(xxx km/h) + (fifty km)/(60 km/h)] = twoscore 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 take been 45 km/h.

[BL] [OL] Circumspection students that the terms speed, average speed, and instantaneous speed are all often referred to but equally speed in everyday language. Emphasize the importance in science to employ right terminology to avoid defoliation and to properly communicate ideas.

Effigy 2.8 During a 30-infinitesimal circular trip to the shop, the full distance traveled is 6 km. The average speed is 12 km/h. The deportation for the round trip is nix, considering at that place was no net change in position.

Worked Example

Calculating Average Speed

A marble rolls v.2 chiliad in 1.8 due south. What was the marble's average speed?

Strategy

We know the distance the marble travels, 5.two one thousand, and the time interval, 1.8 southward. Nosotros tin can utilise these values in the average speed equation.

Discussion

Average speed is a scalar, then nosotros practice non include direction in the respond. We tin check the reasonableness of the reply past estimating: five meters divided by two seconds is 2.5 one thousand/s. Since ii.5 m/s is close to ii.9 m/southward, the respond is reasonable. This is about the speed of a brisk walk, so it besides makes sense.

Practice Bug

9 .

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

1. 40 m/south
2. - twoscore m/southward
3. 0.03 one thousand/s
4. eight.5 m/s

ten .

Cassie walked to her friend's house with an boilerplate speed of 1.40 k/s. The distance between the houses is 205 g. How long did the trip take her?

1. 146 s

2. 0.01 south

3. two.50 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 depict either the average 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.

$$5_{\text{avg}}=\frac{\text{displacement}}{\text{time}}=\frac{\Delta d}{\Delta t}=\frac{d_{\text{f}}-d_0}{t_{\text{f}}-t_0}$$

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

Tips For Success

Information technology is important to keep in heed that the boilerplate speed is non the aforementioned matter every bit the average velocity without its management. Similar nosotros saw with displacement and altitude in the concluding section, changes in direction over a time interval accept a bigger effect on speed and velocity.

Suppose a passenger moved toward the back of a plane with an average velocity of –four g/s. We cannot tell from the average velocity whether the passenger stopped momentarily or backed up before he got to the back of the plane. To go more details, we must consider smaller segments of the trip over smaller time intervals such as those shown in Figure 2.9. If y'all consider infinitesimally minor intervals, you can define instantaneous velocity, which is the velocity at a specific instant in time. Instantaneous velocity and average velocity are the same if the velocity is constant.

Effigy ii.nine The diagram shows a more detailed tape of an aeroplane passenger heading toward the dorsum of the airplane, showing smaller segments of his trip.

Earlier, you take read that altitude traveled can be dissimilar than the magnitude of displacement. In the same style, speed tin can be different than the magnitude of velocity. For example, you drive to a store and return dwelling in one-half an hr. If your motorcar's odometer shows the total distance traveled was 6 km, then your boilerplate speed was 12 km/h. Your average velocity, even so, was nil because your deportation for the round trip is null.

Scout Physics

Computing Average Velocity or Speed

This video reviews vectors and scalars and describes how to calculate average velocity and average speed when y'all know displacement and modify in time. The video also reviews how to convert km/h to m/s.

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

1. A scalar quantity is fully described by its magnitude, while a vector needs both magnitude and management to fully describe information technology. Deportation is an instance 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 draw information technology. Time is an instance of a scalar quantity and deportation is an example of a vector quantity.

3. A scalar quantity is fully described by its magnitude and direction, while a vector needs simply magnitude to fully describe it. Displacement is an example of a scalar quantity and time is an case of a vector quantity.

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

Teacher Back up

Instructor Back up

This video does a good job of reinforcing the difference between vectors and scalars. The student is introduced to the idea of using 's' to denote displacement, which you may or may not wish to encourage. Earlier students sentry the video, point out that the instructor uses $\overrightarrow{s}$ for displacement instead of d, as used in this text. Explain the use of small arrows over variables is a common mode to announce vectors in college-level physics courses. Circumspection students that the customary abbreviations for hour and seconds are non used in this video. Remind students that in their own work they should use the abbreviations h for hour and s for seconds.

Worked Instance

Calculating Boilerplate Velocity

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

Strategy

We know that the deportation is 304 m north and the time is 180 s. Nosotros tin can use the formula for average velocity to solve the problem.

Discussion

Since average velocity is a vector quantity, you must include direction as well equally magnitude in the answer. Find, however, that the direction can be omitted until the end to avoid cluttering the trouble. Pay attention to the meaning figures in the trouble. The altitude 304 m has three pregnant figures, simply the time interval 180 due south has only 2, then the quotient should take just two pregnant figures.

Tips For Success

Note the style scalars and vectors are represented. In this book d represents altitude 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 modest arrows above the variable.

Teacher Support

Teacher Support

Employ this problem to emphasize the importance of using the right number of meaning figures in calculations. Some students have a tendency to include many digits in their final calculations. They incorrectly believe they are improving the accuracy of their answer past writing many of the digits shown on the reckoner. Betoken out that doing this introduces errors into the calculations. In more complicated calculations, these errors can propagate and crusade the final answer to be wrong. Instead, remind students to ever conduct ane or two extra digits in intermediate calculations and to round the final answer to the right number of significant figures.

Worked Example

Solving for Displacement when Average Velocity and Time are Known

Layla jogs with an average velocity of 2.four m/s east. What is her displacement later 46 seconds?

Strategy

We know that Layla's average velocity is 2.4 g/s e, and the time interval is 46 seconds. Nosotros can rearrange the boilerplate velocity formula to solve for the displacement.

Give-and-take

The answer is about 110 m east, which is a reasonable displacement for slightly less than a minute of jogging. A calculator shows the respond as 110.4 yard. We chose to write the answer using scientific notation because nosotros wanted to make information technology clear that we only used two significant figures.

Tips For Success

Dimensional analysis is a skilful mode to determine whether you solved a problem correctly. Write the calculation using only units to be sure they match on contrary sides of the equal mark. In the worked example, you lot have
m = (thou/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 thou and, of course, 1000 = 1000.

Worked Case

Solving for Fourth dimension when Deportation and Average Velocity are Known

Phillip walks along a straight path from his house to his school. How long volition it take him to go to school if he walks 428 m west with an average velocity of ane.7 m/due south west?

Strategy

Nosotros know that Phillip's displacement is 428 m west, and his average velocity is 1.vii m/s west. Nosotros can calculate the fourth dimension required for the trip past rearranging the average velocity equation.

Word

Here again nosotros had to apply scientific notation because the answer could only take two significant figures. Since fourth dimension is a scalar, the answer includes only a magnitude and not a direction.

Do Issues

11 .

A trucker drives along a straight highway for 0.25 h with a deportation of 16 km southward. What is the trucker's average velocity?

1. 4 km/h north

2. 4 km/h s

3. 64 km/h north

4. 64 km/h south

12 .

A bird flies with an boilerplate velocity of seven.5 m/south east from ane branch to another in 2.4 s. It so pauses before flying with an average velocity of 6.viii m/s eastward for 3.5 s to another co-operative. What is the bird's total displacement from its starting point?

1. 42 yard west
2. 6 thou west
3. 6 chiliad east
4. 42 m east

Virtual Physics

The Walking Human

In this simulation yous will put your cursor on the man and motility him outset in i direction and then in the contrary direction. Keep the Introduction tab active. You tin utilise the Charts tab after you learn well-nigh graphing motion later on in this chapter. Carefully sentry the sign of the numbers in the position and velocity boxes. Ignore the dispatch box for now. See if you can make the man'southward position positive while the velocity is negative. Then see if you tin can do the opposite.

Grasp Cheque

Which state of affairs correctly describes when the moving homo'due south position was negative only his velocity was positive?

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

Instructor Back up

Teacher Support

This is a powerful interactive blitheness, and it tin be used for many lessons. At this betoken it can be used to bear witness that displacement can be either positive or negative. Information technology can too bear witness that when deportation is negative, velocity tin can exist either positive or negative. Later it tin can be used to show that velocity and acceleration can have unlike signs. Information technology is strongly suggested that you continue students on the Introduction tab. The Charts tab tin can be used afterwards students learn about graphing motion later in this affiliate.

Check Your Understanding

13 .

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

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

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

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

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

14 .

If you divide the total distance traveled on a machine trip (as adamant by 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. Boilerplate speed. Both are the same when the car is traveling at a constant speed and changing direction.
2. Average 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 same when the auto is traveling at a constant speed.
4. Magnitude of average velocity. Both are same when the automobile does non modify its direction.

15 .

Is it possible for boilerplate velocity to exist negative?

1. Yes, if internet displacement is negative.

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

3. No, because boilerplate velocity describes merely the magnitude and not the direction of motility.

4. No, considering average velocity only describes the magnitude in the positive management of motility.

Instructor Support

Teacher Support

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

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

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