Kinematics

Average Acceleration

Variables

• In addition to the variables previously used to calculate average velocity (vavg), we add one more:

• a- acceleration (m/s2)aavg- average acceleration

Solving for acceleration

• Acceleration can be found 2 ways:

• Graphically- read from a Velocity vs. Time graph

• Mathematically- found using an equation

Graphically

• Imagine a velocity vs time graph:

• Consider the SLOPE of this line.

0 1 2 3 4 5 60

2

4

6

8

10

12

Velocity vs. Time

Time (s)

Velci

ty (m

/s)

Graphically

• The slope is Δv/Δt = (10m/s) / (5s)

• Look at the UNITS of the slope…

0 1 2 3 4 5 60

2

4

6

8

10

12

Velocity vs. Time

Time (s)

Velci

ty (m

/s)

Graphically

0 1 2 3 4 5 60

2

4

6

8

10

12

Velocity vs. Time

Time (s)

Velci

ty (m

/s)

2/2*

25

/10sm

ss

m

s

sm

t

v

Same units as

acceleration.

Graphically

0 1 2 3 4 5 60

2

4

6

8

10

12

Velocity vs. Time

Time (s)

Velci

ty (m

/s)

2/2*

25

/10sm

ss

m

s

sm

t

v

The SLOPE of a VELOCITY vs. TIME graph represents the ACCELERATION of the moving object.

Mathematically

• Formula:

• The formula looks like the slope of the velocity vs. time graph: That is where it comes from.

t

vv

t

va ifavg

Example

• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.

Example

• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.

• Givens: a= -1.8 m/s2 vi= 9.0 m/s vf= 0 m/s (implied)• Unknown: t=?

Example

• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.

• Givens: a= -1.8 m/s2 vi= 9.0 m/s vf= 0 m/s (implied)• Unknown: t=?

• Formula: t

vva ifavg

Example

• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.

• Givens: a= -1.8 m/s2 vi= 9.0 m/s vf= 0 m/s (implied)• Unknown: t=?

• Formula:

ssm

smt

smtsm

t

smsmsm

t

vva ifavg

5/8.1

/0.9

/0.9)/8.1(

/0.9/0/8.1

2

2

2

Practice

• Page 49, Practice B.

• ALL units will be in meters, seconds, and m/s.