VELOCITY-TIME GRAPHS• This lesson will teach you how to draw and

analyze velocity time graphs.• Many aspects of graphical analysis will also be

covered

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By the end of this lesson, you will be able to:

What are we going to cover today?

v-t graphing basics

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Analyze uniform v-t graphsAnalyze non -uniform v-t graphs

Homework

What is the distance? What is the

displacement? What is the speed? What is the velocity?

What are they in km/hr? What is the

acceleration?82.5m

3s

1 secOr33 km/hr

2 secOr66 km/hr

3 secOr99 km/hr

99 - 03 - 0

Velocity-time graph A graph describing the motion of

an objectVelocity = y-axisTime = x-axis Slope = average acceleration

Acceleration a How quickly an objects velocity

changes over time (rate of change)

vector

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The slope of a v-t graph is acceleration, a

The area under a v-t graph is displacement, Dd

y yslope

x x

v vt t

va

t

2 1

2 1

2 1

2 1

v-t GRAPHING BASICSS

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time (s)

7.0

velo

city

(m

/s

[U])

6.05.0

3.0

4.0

1.0

2.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Units of the slope are

m/s/s or m/s2 • units of

acceleration

Area

Units of the area are m• units of displacement

-2.0

-1.0

0

1.0

2.0

3.0

4.0

11 12 13 14

-3.0

-4.0

velo

city

(m

/s

[E])

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.time (s)

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accelerating east

-2.0

-1.0

0

1.0

2.0

3.0

4.0

11 12 13 14

-3.0

-4.0

velo

city

(m

/s

[E])

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.time (s)

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moving east at constant velocity

-2.0

-1.0

0

1.0

2.0

3.0

4.0

11 12 13 14

-3.0

-4.0

velo

city

(m

/s

[E])

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.time (s)

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accelerating westOrNeg. acceleration east

-2.0

-1.0

0

1.0

2.0

3.0

4.0

11 12 13 14

-3.0

-4.0

velo

city

(m

/s

[E])

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.time (s)

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moving west at constant velocity

-2.0

-1.0

0

1.0

2.0

3.0

4.0

11 12 13 14

-3.0

-4.0

velo

city

(m

/s

[E])

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.time (s)

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accelerating east

-2.0

-1.0

0

1.0

2.0

3.0

4.0

11 12 13 14

-3.0

-4.0

velo

city

(m

/s

[E])

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.time (s)

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The x-axis does not represent the origin

The x-axis represents a velocity of zero

PRACTICE QUESTION

1. What is the slope of a v-t graph?

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a. Displacementb. Velocityc. Accelerationd. Positione. None of the above

PRACTICE QUESTION

2. What is the area under a v-t graph?

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a. Displacementb. Velocityc. Accelerationd. Positione. None of the above

PRACTICE QUESTIONS

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3. Which v-t graph depicts no motion?

a. b. c. d.

time (s)

14

velo

city

(m

/s

[U])

12

10.

6.0

8.0

2.0

4.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

time (s)

velocity (m/s [U])

0.0 10.

1.0 10.

2.0 10.

3.0 10.

4.0 10.

5.0 10.

6.0 1o.

UNIFORM VELOCITY-TIME GRAPHS

. .slope

. .

.

10 106 0 1 00 0

Since the accel is zero, the object has a constant velocity

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2 a . m/s [U] 0 0

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Uniform motion is a horizontal line on a v-t graph

time (s)

14

velo

city

(m

/s

[U])

12

10.

6.0

8.0

2.0

4.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

area . m/s [U] . s

. m [U]

10 5 050

s d . m [U] 1 6 50

time (s)

14

velo

city

(m/s

[E

])

12

10.

6.0

8.0

2.0

4.0

1.0

2.0

3.0

time (s)

velocity (m/s [E])

0.0 0.0

1.0 4.0

2.0 8.0

3.0 12.0

NON -UNIFORM VELOCITY-TIME GRAPHS

Notice that the line is not curved. It is a diagonal line

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.slope

. .

.

12 4 03 0 1 04 0

2 a . m/s [E] 4 0

time (s)

14

velo

city

(m

/s

[E])

12

10.

6.0

8.0

2.0

4.0

1.0

2.0

3.0

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totalav

total

dv

t

To determine average speed from a v-t graph we use:

totalav

total

dv

t

To determine average vel from a v-t graph we use:

To determine inst vel from a v-t graph we simply read the vel values on the graph

PRACTICE QUESTIONS

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4. Which v-t graph depicts an object moving at constant velocity?

a. b. c. d.

PRACTICE QUESTION

Plot the velocity time data and answer the following

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time (s)

velocity (m/s [N])

0.0 5.0

1.0 10.

2.0 10.

3.0 5.0

4.0 0.0

5.0 -5.0

6.0 -5.0

7.0 0.0

PRACTICE QUESTION

5. What is the accel of the object between 0 – 1 s?

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a. -2.0 m/s2 [N]b. 2.0 m/s2 [N]c. 5.0 m/s2 [S]d. -5.0 m/s2 [S]

PRACTICE QUESTION

6. When is the object not moving?

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a. Between 1 and 2 s b. Between 5 and 6 sc. Both a and bd. at 4.0 s and 7.0 se. The object never

stops

PRACTICE QUESTION

7. How long was the object stopped?

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a. 1.0 sb. 2.0 sc. 5.0 sd. The object stops for only a brief

momente. The object never stops

PRACTICE QUESTION

8. What is the objects displacement?

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a. 5.0 m [N]b. 18 m [N]c. 5.0 m [S]d. 33 m [N]

PRACTICE QUESTION

9. What is the average speed of the object?

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a. 2.6 m/s [S]b. 2.6 m/s [N]c. 5.4 m/s [S]d. 5.4 m/s [N]e. None of the above

PRACTICE QUESTION

10. What is the average velocity of the object?

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a. 2.6 m/s [N]b. 2.6 m/s [S]c. 5.4 m/s [N]d. 5.4 m/s [S]e. None of the above

HOMEWORKS

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Read pgs 21 – 35

Practice 1 & 2 on pg 29

Questions 1-4 on pg 35