Science 24: Speed/Velocity – How to Calculate it and How to Graph it

How good are you at estimating the speed of the vehicle in which you are travelling? How accurately can you estimate the speed of vehicles while in a parked car or while walking down a sidewalk? In this lesson you will explore how speed is defined.

Speed:

Velocity:

How is Velocity different from Speed?

The formula for calculating average speed is: You can use this formula to calculate distance and time.

v =

∆d =

∆t =

Note: Throughout this module you will use the terms speed and velocity interchangeably to remain consistent with the textbook.

Example

The speed limit on many Alberta highways is 100 km/h.

What is this speed in m/s?

Solution

The velocity of a car travelling 100 km/h is approximately 27.78 m/s.

Example

Jesse used her stopwatch to time a car travelling a distance of 50 m. The car covered this distance in 2 s. How fast was the car travelling in m/s and in km/h?

Solution

Use the formula for velocity.

Unit Conversions revisited: Converting from m/s to km/h:

The System International (SI) units for speed is m/s

More commonly we measure speed in km/h

To convert from m/s to km/h or the other way:

1km = m 1h = s

Convert 5m/s to km/h

Convert 15km/h to m/s

Convert the Answer to m/s

Now, it's your turn. Convert the following.

a. 50 km/h into m/s

b. 50 m/s into km/h

Practice: YOU MUST SHOW YOUR WORK. You can use a calculator but you must show all of the steps involved in doing the problem.

1. Dan walked 12.0m from the bus stop, turned around and walked back 4.0m. Dan walked a total of 16.0m He accomplished this in 20.0s. Find Dan’s speed.

2. The speed limit on some rural roads is 80 km/h. How far would you travel in one hour at that speed?

3. A person runs 3km in 0.5h. What is his speed in km/h? What is his speed in m/s?

4. What is the speed of a jet plane that travels 528 meters in 4 seconds?

5. How long will your trip take (in hours) if you travel 350 km at an average speed of 80 km/hr?

6. To get home, you drive 25 km in 20 minutes, what is your speed? Convert your final answer to meters/second

7. Fill out the chart; use a spare piece of paper to calculate answers.

Locations Distance Time Speed

Edmonton to Red Deer 1.35 h 110 km/h

Red Deer to Calgary 1.33 h 110 km/h

Calgary to Banff 159 km 1.76 h

Banff to Lake Louise 56 km 0.62 h

Lake Louis to Jasper 289 km 3.2 h

Jasper to Hinton 272.8 km 100 km/h

SPEED

1. If a car travels 400m in 20 seconds how fast is it going?

2. If you move 50 meters in 10 seconds, what is your speed?

3. You arrive in my class 45 seconds after leaving math which is 90 meters away. How fast did you travel?

4. A plane travels 395,000 meters in 9000 seconds. What was its speed?

5. It takes Serina 0.25 hours to drive to school. Her route is 16 km long. What is Serina’s average speed on her drive to school?

TIME

6. How much time will it take for a bug to travel 5 meters across the floor if it is traveling at 1 m/s?

7. You need to get to class, 200 meters away, and you can only walk in the hallways at about 1.5 m/s. (if you run any faster, you’ll be caught for running). How much time will it take to get to your class?

8. In a competition, an athlete threw a flying disk 139 meters through the air. While in flight, the disk traveled at an average speed of 13.0 m/s. How long did the disk remain in the air?

DISTANCE

9. How far can you get away from your little brother with the squirt gun filled with paint if you can travel at 3 m/s and you have 15s before he sees you?

10. How far can your little brother get if he can travel at 2.5 m/s and in 5 seconds you will discover that his squirt gun has run out of paint?

Graphing Speed

An average speed graph plots distance vs. time Time is the manipulated variable and is plotted on the “x” axis Distance is the responding variable and is plotted on the “y” axis The steeper the slope of the line, the faster the object is traveling. Average speed can be determined by finding the slope of the line that you have drawn

Examples :

A polar bear is travelling 5 km/h through its territory. After 1 h, it covered 5 km; after 2 h, it covered 10 km; and so on. A biologist studying the polar bear graphed the distance it travelled every hour for five hours. She plotted time on the x-axis (horizontal axis) and distance on the y-axis (vertical axis). This graph, shown below, is an example of a distance/time graph.

Use the graph on the right to answer questions (a) to (c).

(a) How far does Car A travel every hour? What is its velocity?

(b) How far does Car B travel every hour? What is its velocity.

(c) Which graph has the steeper slope? What does a steeper slope tell you?

Calculating Slope

Example:

Time (s) 0 2.0 4.0 6.0 8.0 10.0

Distance Travelled (m) 0 10 20 30 40 50

Slope = rise/run

= change in distance = ∆d

change in time ∆t

= 30m – 10m

6.0s - 2.0s

= 20m = 5.0m/s

4.0s

What you were actually finding was v = ∆d/∆t

Turn to pages 260 and 261 of the textbook. Read the discussion in "Calculating Velocity from a Distance/Time Graph." Then study the procedure in "Math Connect: Slope Formula," and work through the sample problem. Remember, time is on the x-axis and distance is on the y-axis.

14. For the line between two points on a distance/time graph, what does the run represent?

15. For the line between two points on a distance/time graph, what does the rise represent?

16. How is slope defined?

17. For the line between two points on a distance/time graph, what does the slope represent?

4. What is the go-kart's speed?

5. How can you tell from the graph that the go-kart's speed is constant?

. Complete the following table for the dune buggy. You will have to estimate the distances. The time for each period is 1 s.

Go Kart Time Period Distance Travelled Speed

from t = 0 s to t = 1 s 7 m (7 m - 0 m) 7 m/s

from t = 1 s to t = 2 s 10 m (17 m - 7 m)

from t = 2 s to t = 3 s

from t = 3 s to t = 4 s

from t = 4 s to t = 5 s

Dune Buggy Time Period Distance Travelled Speed

from t = 0 s to t = 1 s

from t = 1 s to t = 2 s

from t = 2 s to t = 3 s

from t = 3 s to t = 4 s

from t = 4 s to t = 5 s

7. When was the dune buggy travelling the fastest? the slowest? How can you tell just by looking at the graph?

Practice:

Directions: Using the data in the following table, construct a graph of distance vs. time. Then answer the questions about that graph.

1. Does this graph represent constant or changing speed? How do you know?

2. Find the slope of the line and find the average speed.

3. Does this graph represent constant or changing speed? How do you know?

4. Which section of the graph represents the highest speed

Distance (m) Time (sec)

10 20

20 40

35 70

65 130

85 170

100 200

Distance (m) Time (sec)

15 20

25 50

40 65

70 130

90 185

100 200

Graphing Paper Section: