CHAPTER 2 ACCELERATION

CONSTANT vs CHANGING SPEED

Constant Speed occurs when an object covers the same distance in equal intervals of time.

Changing Speed occurs when an object covers different distance in equal intervals of time.

CONSTANT vs. CHANGING VELOCITY

Constant Velocity occurs when an object covers the same displacement in equal intervals of time.

Changing Velocity occurs when an object covers different displacement in equal intervals of time.

CONSTANT VELOCITY

05

1015202530

1 2 3 4Time (s)

Posit

ion

(m)

Constant Velocity Graph

constant velocity

CHANGING VELOCITY

0

5

10

15

20

1 2 3 4Time (s)

Posit

ion

(m)

Changing Velocity Graph

velocity

ACCELERATION

Acceleration will take place if there is a change in direction or speed of a moving object.

ACCELERATIONAcceleration is the rate of changeof velocity.

if

if

ttvv

--

interval Time velocityonAccelerati

timeinitialttimefinalt

velocityinitialvvelocityfinalv

if

if

Observe the animation of the three cars below. Which car or cars (red, green, and/or blue) are undergoing acceleration?

0

5

10

15

20

1 2 3 4

0

2

4

6

8

1 2 3 4Velo

city

(m/s

)

Time (s) Time (s)Velo

city

(m/s

)

PRACTICE PROBLEM 1A car’s velocity changes from 0 m/s to 30 m/s in 10 s. Calculate the car’s acceleration.

2/310

/030

a

smssm

ttvv

if

if

A car’s velocity changes from 10 km/h to 30 km/h, 30 min later. Calculate the car’s acceleration.

PRACTICE PROBLEM 2

2

if

if

if

i

f

h/km40h5.

h/km1030ttvva

h5.0min30tth/km10vh/km30v

Acceleration is positive

Acceleration is negative

Acceleration is positive

Acceleration is negative

Positive or Negative acceleration

In Example A, the object is moving in the positive direction (i.e., has a positive velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object has a positive acceleration.

In Example B, the object is moving in the negative direction (i.e., has a negative velocity) and is slowing down. When an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object also has a positive acceleration.

1-D Constant Acceleration Equations

Vf = Vi + atDf = Vit + ½ at2

Vf2 = vi

2 + 2a(Df-Di)

Problem #1If a car accelerates from rest at

a constant 4.2 m/s2, how long will it take for the car to reach a velocity of 37 m/s?

Problem #1 Solution

2/2.4

/37/0

:

sma

smVsmV

Given

f

i

?

:tUnknown

Problem #1 Solution

atVVOR

tVV

a

Equation

if

if

:

Problem #1 Solution

tsmsmsm

Substitute/0/37/2.4

:

2

stSolve

81.8:

Problem #2An airplane starts from rest

and accelerates at a constant 2.50 m/s2 for 30.0 s before leaving the ground. How far did the airplane move before leaving the ground?

Problem #2 Solution

stsma

smVGiven

i

0.30/50.2

/0:

2

?:

fDUnknown

Problem #2 Solution

2

21

:

attVD

Equation

if

Problem #2 Solution

22 )0.30)(/50.2(21)0.30)(/0(

:

ssmssmD

Substitute

f

mDSolve

f 1125:

Problem #3A parachutist descending at a speed of 10.50 m/s loses a shoe at an altitude of 38.50 m. What is the velocity of the shoe just before it hits the ground if it’s acceleration is 9.8 m/s2?

Problem #3 Solution

mDDsma

smVGiven

if

i

50.38/8.9

/50.10:

2

?:

fVUnknown

Problem #3 Solution

)(2

:22

ifif DDaVV

Equation

Problem #3 Solution

)50.38)(/80.9(2)/50.10(

:222 msmsmV

Substitute

f

smV

V

V

Solve

f

f

f

/4.29

85.864

6.75425.110

:

2

2

CHAPTER 2FREE FALL

ACCELERATION

Free Fall with Air

Resistance

Free Fallwithout

AirResistance

Video Clips

http://www.smgaels.org/physics/home/videos/ForceMotion/freeFallPlot.html

Free Fall Displacement:

How does mass affect free fall?:http://www.smgaels.org/physics/home/videos/ForceMotion/massFreeFall.html

Moon hammer/feather drop:http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html