An Introduction to Acceleration: Learning Goal The student will solve example questions related to uniformly accelerated motion. (B2.7, B3.3) The student.

An Introduction to An Introduction to Acceleration: Learning GoalAcceleration: Learning Goal The student will solve example The student will solve example

questions related to uniformly questions related to uniformly accelerated motion. (B2.7, B3.3)accelerated motion. (B2.7, B3.3)

“It goes from zero to 60 in about 3 seconds.”

An Introduction An Introduction to Accelerationto Acceleration

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AccelerationAcceleration

Acceleration is defined as the change Acceleration is defined as the change in the velocity of an object per in the velocity of an object per interval of time, or:interval of time, or:

AccelerationAcceleration

Acceleration is defined as the change Acceleration is defined as the change in the velocity of an object per in the velocity of an object per interval of time, or:interval of time, or:

t

va

AccelerationAcceleration

Acceleration is defined as the change Acceleration is defined as the change in the velocity of an object per in the velocity of an object per interval of time, or:interval of time, or:

t

vv

t

va

12

AccelerationAcceleration

Acceleration is defined as the change in Acceleration is defined as the change in the velocity of an object per interval of the velocity of an object per interval of time, or:time, or:

vv22 = final velocity and = final velocity and vv11 = initial velocity = initial velocity

t

vv

t

va

12

AccelerationAcceleration

Acceleration will have units of m/s/s or Acceleration will have units of m/s/s or m/sm/s22..

(Notice also that acceleration is a (Notice also that acceleration is a vector.)vector.)

t

vv

t

va

12

Example 1Example 1

Jake increases his velocity from 13 m/s [E] Jake increases his velocity from 13 m/s [E] to 25 m/s [E] in 5.0 s. What is his to 25 m/s [E] in 5.0 s. What is his acceleration?acceleration?

Example 1Example 1

Jake increases his velocity from 13 m/s [E] Jake increases his velocity from 13 m/s [E] to 25 m/s [E] in 5.0 s. What is his to 25 m/s [E] in 5.0 s. What is his acceleration?acceleration?

?

:

0.5

][25

][13

:

2

1

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Ev

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Example 1Example 1

Jake increases his velocity from 13 m/s [E] Jake increases his velocity from 13 m/s [E] to 25 m/s [E] in 5.0 s. What is his to 25 m/s [E] in 5.0 s. What is his acceleration?acceleration?

?

:

0.5

25

13

:

2

1

a

Unknown

st

v

v

Givens

sm

sm

Example 1Example 1

Jake increases his velocity from 13 m/s [E] Jake increases his velocity from 13 m/s [E] to 25 m/s [E] in 5.0 s. What is his to 25 m/s [E] in 5.0 s. What is his acceleration?acceleration?

24.20.5

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12

sms

msm

sa

t

vva

?

:

0.5

25

13

:

2

1

a

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Example 1Example 1

Jake increases his velocity from 13 m/s [E] to Jake increases his velocity from 13 m/s [E] to 25 m/s [E] in 5.0 s. What is his 25 m/s [E] in 5.0 s. What is his acceleration?acceleration?

His acceleration is 2.4 m/sHis acceleration is 2.4 m/s22 [E].[E].

24.20.5

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12

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msm

sa

t

vva

?

:

0.5

25

13

:

2

1

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Example 2Example 2

Richard reduces his velocity from 15 m/s Richard reduces his velocity from 15 m/s [forward] to 12 m/s [forward] in 4.0 s. [forward] to 12 m/s [forward] in 4.0 s. What is his acceleration?What is his acceleration?

Example 2Example 2

Richard reduces his velocity from 15 m/s Richard reduces his velocity from 15 m/s [forward] to 12 m/s [forward] in 4.0 s. [forward] to 12 m/s [forward] in 4.0 s. What is his acceleration?What is his acceleration?

?

:

0.4

12

15

:

2

1

a

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v

v

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sm

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Example 2Example 2

Richard reduces his velocity from 15 m/s Richard reduces his velocity from 15 m/s [forward] to 12 m/s [forward] in 4.0 s. [forward] to 12 m/s [forward] in 4.0 s. What is his acceleration?What is his acceleration?

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sms

msm

sa

t

vva

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:

0.4

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15

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Example 2Example 2

Richard reduces his velocity from 15 m/s Richard reduces his velocity from 15 m/s [forward] to 12 m/s [forward] in 4.0 s. What [forward] to 12 m/s [forward] in 4.0 s. What is his acceleration?is his acceleration?

His acceleration is 0.75 m/sHis acceleration is 0.75 m/s22 [backward].[backward].

275.00.4

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sms

msm

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t

vva

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:

0.4

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15

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Rearranging the Rearranging the EquationEquation

The equation that The equation that represents the represents the definition of definition of acceleration may acceleration may be rearranged to be rearranged to solve for any of solve for any of the other the other variables, e.g.variables, e.g.

(solving for (solving for vv22))

Rearranging the Rearranging the EquationEquation

The equation that The equation that represents the represents the definition of definition of acceleration may acceleration may be rearranged to be rearranged to solve for any of solve for any of the other the other variables, e.g.variables, e.g.

Rearranging the Rearranging the EquationEquation

The equation that The equation that represents the represents the definition of definition of acceleration may acceleration may be rearranged to be rearranged to solve for any of solve for any of the other the other variables, e.g.variables, e.g.

Rearranging the Rearranging the EquationEquation

The equation that The equation that represents the represents the definition of definition of acceleration may acceleration may be rearranged to be rearranged to solve for any of solve for any of the other the other variables, e.g.variables, e.g.

Rearranging the Rearranging the EquationEquation

The equation that The equation that represents the represents the definition of definition of acceleration may acceleration may be rearranged to be rearranged to solve for any of solve for any of the other the other variables, e.g.variables, e.g.

Rearranging the Rearranging the EquationEquation

The equation that The equation that represents the represents the definition of definition of acceleration may acceleration may be rearranged to be rearranged to solve for any of solve for any of the other the other variables, e.g.variables, e.g.

tavvor

vvta

vvvvta

vvta

tt

vvta

t

vva

12

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Example 3Example 3

A ball is travelling at 12 m/s [up] and being A ball is travelling at 12 m/s [up] and being accelerated at 9.8 m/saccelerated at 9.8 m/s22 [down]. What is [down]. What is its velocity after 2.0 s?its velocity after 2.0 s?

?

:

0.2

8.9

12

:

2

1

2

v

Unknown

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a

v

Givens

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Example 3Example 3

A ball is travelling at 12 m/s [up] and being A ball is travelling at 12 m/s [up] and being accelerated at 9.8 m/saccelerated at 9.8 m/s22 [down]. What is [down]. What is its velocity after 2.0 s?its velocity after 2.0 s?

?

:

0.2

8.9

12

:

2

1

2

v

Unknown

st

a

v

Givens

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Example 3Example 3

A ball is travelling at 12 m/s [up] and being A ball is travelling at 12 m/s [up] and being accelerated at 9.8 m/saccelerated at 9.8 m/s22 [down]. What is [down]. What is its velocity after 2.0 s?its velocity after 2.0 s?

?

:

0.2

8.9

12

:

2

1

2

v

Unknown

st

a

v

Givens

sm

sm

sm

sm

sm svSolve

tavvt

vvaSelect

6.7)0.2)(8.9(12:

:

22

1212

Example 3Example 3

A ball is travelling at 12 m/s [up] and being A ball is travelling at 12 m/s [up] and being accelerated at 9.8 m/saccelerated at 9.8 m/s22 [down]. What is [down]. What is its velocity after 2.0 s?its velocity after 2.0 s?

Its velocity is 7.6 m/s Its velocity is 7.6 m/s [down].[down].?

:

0.2

8.9

12

:

2

1

2

v

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a

v

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tavvt

vvaSelect

6.7)0.2)(8.9(12:

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More PracticeMore Practice

Playing with the Ticker Timers and Playing with the Ticker Timers and AccelerationAcceleration

Graphing AccelerationGraphing Acceleration