problem solving speed and velocity worksheet

2.2 Speed and Velocity

Section learning objectives.

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

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

Teacher Support

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

• (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 Manual addresses content in this section in the lab titled: Position and Speed of an Object, as well as the following standards:

Section Key Terms

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 often used interchangeably in everyday life, but their scientific definitions are different. Tell students that they will learn about these differences as they read the section.

[AL] Explain to students that velocity, like displacement, is a vector quantity. Ask them to speculate about ways that speed is different from velocity. After they share their ideas, follow up with questions that deepen their thought process, such as: Why do you think that? What is an example? How might apply these terms to motion that you see every day?

There is more to motion than distance and displacement. 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 section we will look at time , speed, and velocity to expand our understanding of motion.

A description of how fast or slow 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 but not a direction. Because speed is a rate, it depends on the time interval of motion. You can calculate the elapsed time or the change in time, Δ t Δ t , of motion as the difference between the ending time and the beginning time

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

When you describe an object's speed, you often describe the average over a time period. Average speed , v avg , is the distance traveled divided by the time during which the motion occurs.

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

Suppose, for example, a car travels 150 kilometers in 3.2 hours. Its average speed for the trip is

A car's speed would likely increase and decrease many times over a 3.2 hour trip. Its speed at a specific instant in time, however, is its instantaneous speed . A car's speedometer describes its instantaneous speed.

[OL] [AL] Caution students that average speed is not always the average of an object's initial and final speeds. For example, suppose a car travels a distance of 100 km. The first 50 km it travels 30 km/h and the second 50 km it travels at 60 km/h. Its average speed would be distance /(time interval) = (100 km)/[(50 km)/(30 km/h) + (50 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, 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.

Worked Example

Calculating average speed.

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

We know the distance the marble travels, 5.2 m, and the time interval, 1.8 s. We can use these values in the average speed equation.

Average speed is a scalar, so we do not include direction in the answer. We can check the reasonableness of the answer by estimating: 5 meters divided by 2 seconds is 2.5 m/s. Since 2.5 m/s is close to 2.9 m/s, the answer is reasonable. This is about the speed of a brisk walk, so it also makes sense.

Practice Problems

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

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. Average velocity is displacement divided by the time over which the displacement occurs.

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

Tips For Success

It is important to keep in mind that the average speed is not the same thing as the average velocity without its direction. Like we saw with displacement and distance in the last section, changes in direction over a time interval have a bigger effect 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 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 as those shown in Figure 2.9 . If you consider infinitesimally small 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.

Earlier, you have read that distance traveled can be different than the magnitude of displacement. In the same way, speed can be different than the magnitude of velocity. For example, you drive to a store and return home in half an hour. If your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero because your displacement for the round trip is zero.

Watch Physics

Calculating average 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 time. The video also reviews how to convert km/h to m/s.

• A scalar quantity is fully described by its magnitude, while a vector needs both magnitude and direction to fully describe it. Displacement is an example of a scalar quantity and time is an example of a vector quantity.
• A scalar quantity is fully described by its magnitude, while a vector needs both magnitude and direction to fully describe it. Time is an example of a scalar quantity and displacement is an example of a vector quantity.
• A scalar quantity is fully described by its magnitude and direction, while a vector needs only magnitude to fully describe it. Displacement is an example of a scalar quantity and time is an example of a vector quantity.
• A scalar quantity is fully described by its magnitude and direction, while a vector needs only magnitude to fully describe it. Time is an example of a scalar quantity and displacement is an example of a vector quantity.

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. Before students watch the video, point out that the instructor uses s → s → for displacement instead of d, as used in this text. Explain the use of small arrows over variables is a common way to denote 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 use the abbreviations h for hour and s for seconds.

Calculating Average Velocity

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

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

Since average velocity is a vector quantity, you must include direction as well as 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 problem. The distance 304 m has three significant figures, but the time interval 180 s has only two, so the quotient should have only two significant figures.

Note the way scalars and vectors are represented. In this book d represents distance and displacement. Similarly, v 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 by small arrows above the variable.

Use 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 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 can propagate and cause the final answer to be wrong. Instead, remind students to always carry one or two extra digits in intermediate calculations and to round the final answer to the correct number of significant figures.

Solving for Displacement when Average Velocity and Time are Known

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

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

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

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 example, 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 m and, of course, m = m.

Solving for Time when Displacement and Average Velocity are Known

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

We know that Phillip's displacement is 428 m west, and his average velocity is 1.7 m/s west. We can calculate the time required for the trip by rearranging the average velocity equation.

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

• 4 km/h north
• 4 km/h south
• 64 km/h north
• 64 km/h south

A bird flies with an average velocity of 7.5 m/s east from one branch to another in 2.4 s. It then pauses before flying with an average velocity of 6.8 m/s east for 3.5 s to another branch. What is the bird’s total displacement from its starting point?

Virtual Physics

The walking man.

In this simulation you will put your cursor on the man and move him first in one direction and then in the opposite direction. Keep the Introduction tab active. You can use the Charts tab after you learn about graphing motion later in this chapter. Carefully watch the sign of the numbers in the position and velocity boxes. Ignore the acceleration box for now. See if you can make the man’s position positive while the velocity is negative. Then see if you can do the opposite.

Grasp Check

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

• Man moving toward 0 from left of 0
• Man moving toward 0 from right of 0
• Man moving away from 0 from left of 0
• Man moving away from 0 from right of 0

This is a powerful interactive animation, and it can be used for many lessons. At this point it can be used to show that displacement can be either positive or negative. It can also show that when displacement is negative, velocity can 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 keep students on the Introduction tab. The Charts tab can be used after students learn about graphing motion later in this chapter.

Check Your Understanding

• Yes, because average velocity depends on the net or total displacement.
• Yes, because average velocity depends on the total distance traveled.
• No, because the velocities of both runners must remain exactly the same throughout the journey.
• No, because the instantaneous velocities of the runners must remain the same at the midpoint but can vary at other points.

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

• Average speed. Both are the same when the car is traveling at a constant speed and changing direction.
• Average speed. Both are the same when the speed is constant and the car does not change its direction.
• Magnitude of average velocity. Both are same when the car is traveling at a constant speed.
• Magnitude of average velocity. Both are same when the car does not change its direction.
• Yes, if net displacement is negative.
• Yes, if the object’s direction changes during motion.
• No, because average velocity describes only the magnitude and not the direction of motion.
• No, because average velocity only describes the magnitude in the positive direction of motion.

Use 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 will help identify which and direct students to the relevant content. Assessment items in TUTOR will allow you to reassess.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-physics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/physics/pages/1-introduction

• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: Physics
• Publication date: Mar 26, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/physics/pages/1-introduction
• Section URL: https://openstax.org/books/physics/pages/2-2-speed-and-velocity

© Jan 19, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

speed and acceleration worksheets

All Formats

Resource types, all resource types.

• Rating Count
• Price (Ascending)
• Price (Descending)
• Most Recent

Speed and acceleration worksheets

Calculating and Graphing Speed , Velocity, and Acceleration . Quiz or Worksheet

Speed , Velocity, and Acceleration - Worksheet | Easel Activity & Printable PDF

• Easel Activity

Distance, Displacement, Speed , Velocity & Acceleration Worksheet Bundle

Speed , Velocity, and Acceleration - Worksheet | Printable and Distance Learning

• Google Apps™

Speed , Velocity, and Acceleration Worksheet - Engaging Cut and Glue

Speed Velocity and Acceleration Motion Maze Worksheet Assessment Activity

Speed Velocity Acceleration and Graphing Worksheets

Matching Speed and Acceleration Graphs Matching Worksheets , Card Sorts with Key

Speed , Velocity, Acceleration Activities & Worksheets : PPT, PDF, Google SlidesTM

Speed & Acceleration (Physics worksheet )

Review - Motion: Speed , Velocity, Acceleration , and Momentum Worksheet

Speed , Velocity, & Acceleration MATH Worksheets (Package of 6 Worksheets )

Speed , Velocity and Acceleration BUNDLE of Reading Notes, Task Cards, Worksheets

Speed and Acceleration Practice Worksheet

Speed , Velocity, and Acceleration Review Worksheet

Speed , Velocity, & Acceleration Physics Worksheet

Speed Velocity and Acceleration Problems Worksheet

Calculating Speed , Acceleration , and Momentum Practice Worksheet

• Google Drive™ folder

Speed , Velocity, and Acceleration Worksheet

Interpreting Motion Diagrams With Speed and Acceleration : A Physics Worksheet

Speed , Velocity and Acceleration _NO PREP REVIEW WORKSHEETS

Speed and Acceleration Worksheet / Homework

• Word Document File

Worksheet : Speed Velocity and Acceleration Calculations

• Google Docs™
• We're hiring
• Help & FAQ
• Privacy policy
• Student privacy
• Terms of service
• Tell us what you think

Child Login

• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
• More Number Sense Worksheets
• Size Comparison
• Measuring Length
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature
• More Measurement Worksheets
• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
• Box-and-whisker Plot
• Permutation and Combination
• Probability
• Venn Diagram
• More Statistics Worksheets
• Shapes - 2D
• Shapes - 3D
• Lines, Rays and Line Segments
• Points, Lines and Planes
• Transformation
• Quadrilateral
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
• Surface Area
• Pythagorean Theorem
• More Geometry Worksheets
• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Squaring Numbers
• Square Roots
• Scientific Notations
• Speed, Distance, and Time
• Absolute Value
• More Pre-Algebra Worksheets
• Translating Algebraic Phrases
• Evaluating Algebraic Expressions
• Simplifying Algebraic Expressions
• Algebraic Identities
• Quadratic Equations
• Systems of Equations
• Polynomials
• Inequalities
• Sequence and Series
• Complex Numbers
• More Algebra Worksheets
• Trigonometry
• Math Workbooks
• English Language Arts
• Summer Review Packets
• Social Studies
• Holidays and Events
• Worksheets >
• Pre-Algebra >

Speed, Distance, and Time Worksheets

Pacy and fun, our pdf speed, distance, and time worksheets ensure children in grade 6, grade 7, and grade 8 have what it takes to remain well ahead of their peers! Let them use the given measures and apply the correct formula to obtain the unknown measure. Hold the child spellbound with sure-to-help-upskill printables that drive them to complete the tables, answer MCQs, solve word problems, and compare speeds. Step in and take the helms with our free speed, time, and distance worksheets!

Finding the Speed | Level 1

Remind the learners that speed = distance / time. Children must write the speeds, choose the correct alternatives while answering MCQs, and complete the table by working out the missing measures.

• Download the set

Finding the Speed | Level 2

A moderately difficult pdf worksheet, this resource empowers children to find speed hammer and tongs. Help them effectively divide the distance by time and round the speed to the nearest whole number.

Finding the Speed | Word Problems

Watch your practice flourish with a flurry of problems in finding the rate which a person or object covers a distance at! Divide the distance covered by the time taken to obtain the speed in these printables.

Finding the Distance | Level 1

Students know that distance = speed x time. They have bags of time to figure how to find the distance working with a bunch of easy exercises. Use the included answer key to double-check the solutions.

Finding the Distance | Level 2

Introduce 7th grade and 8th grade learners to these pdf worksheets and let them solve intriguing exercises involving 2-digit and 3-digit speeds. This level includes the time format X hours Y minutes.

Finding the Distance | Word Problems

Get children aspiring to grab more of our speed, distance, and time worksheets to calculate the distance given the speed and time. Interactive and easy, the word problems draw on real-life scenarios.

Finding the Time

How easy is it to find the time when the speed and distance are known? Check it out! Practice finding the time by employing the formula time = distance / speed and remain head and shoulders above others.

Finding the Time | Word Problems

It’s time to test skills in finding the time using distance and speed! Get tons of realistic scenarios to calculate the time taken. Our word problems, a breath of fresh air, help hammer home the concept of time!

Mixed Revision Worksheets

Blend learning with excitement with this section of speed, distance, and time worksheets! Guide children to find one of the three measures given the other two. Be as consistent and correct as possible.

Mixed Revision | Word Problems

An eclectic mix of word problems, these printable mixed revision worksheets ensure students are on the ball from the get-go! Read each problem, analyze the given measures, and find the unknown one.

Comparing Speeds

Set grade 6, grade 7, and grade 8 children an exciting challenge to solve exercises and compare speeds! These pdf tools focus on finding who (person) or which (object) is faster given the distance and time.

Conversion of Units of Speed

A reliable companion that makes conversion among speeds - m/s, km/h, and mph - a breeze, these printables are teeming with a mix of easy and difficult exercises. Stay attentive as you forge ahead!

(15 Worksheets)

Related Worksheets

» U.S. Customary Unit Conversion

» Metric Unit Conversion

» Time Conversion

» Solved Examples on Finding Speed

Become a Member

Membership Information

Privacy Policy

What's New?

Printing Help

Testimonial

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

JEE-IIT-NCERT Physics & Math

Widget atas posting, average velocity and average speed problems and solutions.

  Problem #1

Post a Comment for "Average Velocity and Average Speed Problems and Solutions"