More One-Dimensional Kinematics

Unit 1 Presentation 4

Remember Our Kinematic Equations

tvvd

t

va

t

dv

tatvdd

davv

tavv

fo

oof

of

of

2

1

2

1

)(2

2

22

)(

.

.

.

.

changedelta

timet

ntdisplacemeinitiald

ntdisplacemefinald

onacceleratia

velocityinitialv

velocityfinalv

o

f

o

f

Kinematics Example Problems

A car accelerates from rest to a speed of 10 m/s over 15 seconds. What was the acceleration of the car?

sec15

/10

/0

?

t

smv

smv

a

f

o atvv of

2/67.0sec15

/0/10sm

smsma

t

vv of

Another Kinematics Example Problem

Now find the distance it took the car in the previous problem to reach its final velocity of 10 m/s.

?

sec15

/10

/0

/67.0 2

d

t

smv

smv

sma

f

o

advv of 222

msm

smsmd

a

vv of 6.74)/67.0(2

)/0()/10(

2 2

2222

An Alternative Way to Solve the Same Problem

?

0

sec15

/10

/0

/67.0 2

f

o

f

o

d

md

t

smv

smv

sma

2

2

1attvdd oof

msmd f 6.74sec)15)(/67.0(2

1sec)15(00 22

Free Fall

Free fall occurs when the initial velocity in the y-direction is equal to zero. Think of simply dropping an object.

2

2

1attvhh oof

Lets look at the “big” kinematic equation and simplify it, solving for time:

2

2

1)(00 gtth

g

ht

2

Now, consider the only acceleration in the y-direction is the acceleration due to gravity (g) and the initial height is 0 meters:

More on Free Fall

Notice that the free fall equation is only dependent on height and the acceleration due to gravity. NOT dependent on mass! Hence, in the absence of air resistance

and friction, any two objects dropped from the same height will impact the ground at exactly the same time.

Including a bowling ball and a feather!

Free Fall Example Problem

Calculate the time it takes for a ball to drop 10 meters.

?

/8.9

102

t

smg

mh

sec43.1/8.9

)10(222

sm

m

g

ht

Free Fall Example Problem

Calculate the time it takes for a ball to drop 100 meters.

?

/8.9

1002

t

smg

mh

sec52.4/8.9

)100(222

sm

m

g

ht

Another Kinematics Example

A typical jetliner lands at a speed of 160 mi/hr and decelerates at a rate of (10 mi/hr)/sec. If the plane travels at a constant speed of 160 mi/hr for 1.0 sec after landing before applying the breaks, what is the total displacement of the aircraft between touchdown on the runway and coming to rest?

2/47.4sec3600

1

1

1000

1

6.1

sec

1)0.10(

/5.71sec3600

1

1

1000

1

6.1160

smhr

km

m

mi

km

hr

mia

smhr

km

m

mi

km

hr

mivo

First, lets convert all of our units to the SI system:

msmattvx ocoasting 5.710sec)00.1)(/5.71(2

1 2

Now find the displacement while the plane is coasting (no accel):

smv

t

f /0

sec00.1

Another Kinematics Example Cntd.

Now, find the displacement while the plane is breaking:

msm

sm

a

vvx

xavv

ofbreaking

breakingof

572)/47.4(2

)/5.71(0

2

2

2

222

22

Now, to find the total displacement, add the coasting and breaking displacements:

mmmxx breakingcoasting 64457272