phys10-chap2-1dmotion

7/26/2019 Phys10-Chap2-1DMotion

1/7

MOTION IN STR IGHT LINE

-> change in position (x, y, z)

2

0m 1m 2m 3m 4mx

-1m-2m-3m-4m

0xxx

final position

initial position

Example: Find the change in position of the skier.

m5m)2()m3( x

-

> change in position with respect to change in time

3

0m 1m 2m 3m 4mx

-1m-2m-3m-4m

0

0)(

tt

xx

t

xv

xave

Example: Find the average velocity of the skier.

sm1

0s5sm)2(m3

t

xvave

00t s5t

2

0)(

xx

xave

vv

v

4

s

m5.7

2

)5()10(

2

sm

sm

0

ave

xx

ave

v

vv

v

s

m5

0

xv

s

m10

xv

Example: Find the average velocity of the skier.

+v

-

> moving towards +x axis

-

v

-

>

moving

towards

-

x

axis

v


2/7

-> velocity at a certain instant or moment

5

dt

tdx

t

xtv

t

)(lim)(

0

Example:

5s.and2safterandstartat thevelocityandpositionitsfind

s

m1

s

m9)(

ason timedependspositionsobject'anIf

2

2 tttx

Solution:

At the start (t=0s)

0m)s0(s

m1)s0(

s

m9 2

2

x

6

ttv

2s

m2

s

m9)(

i

nstantaneous velocity

s

m9)s0(

s

m2

s

m9

2

v

After 2s (t=2s)

m22)s2(s

m1)s2(

s

m9 2

2

x

s

m13)s2(

s

m2

s

m9

2

v

After 5s (t=5s)

m70)s5(s

m1)s5(

s

m9 2

2

x

s

m19)s5(

s

m2

s

m9

2

v

7

2s

2m

4m

6m

4s 6s 8st

x

A

B C

D

E

)(BA v

)ero(CB vz

)(DC v

)(undefinedED

)(velocityt

xs

lope of the graph

elocityconstant v

line

8

2s

2m

4m

6m

4s 6s 8st

x

A

B

1v

2v

velocitychanging

curve

acceleration


3/7

-> change in velocity with respect to change in time (

m/s

2)

9

0

0

tt

vv

t

va

xxx

x

Example: Find the average acceleration of the skier.

2

sm

sm

0

0

s

m1

s0s5

510

tt

vva

xx

+a

-

> speeding up

directed towards +x axis

s

m5

0

xv s00 t

s

m10

xv s5t

a

10

Example: Find the average acceleration of the skier.

2

sm

sm

0

0

s

m1

s0s5

105

a

tt

vva xx

-

a

-

> slowing down (deceleration)

directed

towards

-

x axis

s

m10

0

xv s00 t

s

m5

xv s5t

a

11

2s

2m

4m

6m

4s 6s 8st

x

A

B

1v

2v

A to B -> increasing velocity

(

+

acceleration)

B to A -> decreasing velocity

(-

acceleration)

12

2s

2m/s

4m/s

6m/s

4s 6s 8st

vx

A

B C

D

E

)(BA a

)ero(CB az

)(DC a

)(undefinedED

ion)(acceleratt

vx

s

lope of the graph

onacceleraticonstant

line


4/7

13

2s

2m/s

4m/s

6m/s

4s 6s 8st

vx

A

B

1a

2a

curve -

> changing acceleration

A to B -> increasing acceleration

B to A -> decreasing acceleration

14

1. The

distance

from

your

house

to

CSU

is

5

km

and

your

first

subject

is

at

7:

30

AM.

If

you

ride

ajeepney (w/ an average velocity of 7

m/s) starting at your house at7:

20

AM,

will you

be l

ate

for

your

class?

2. You

normally

drive

on

the

freeway

between

Gaisano

and

CSU

at

an

average

speed

of

8

m/s

andthe

trip

takes

15

min.

On

a

Friday

afternoon,

however,

heavy

traffic

slows

you

down

and you

drive

the

same

distance

at

an

average

speed

of

only

5

m/s.

How

much l

onger

does

the

trip

take?

3. An

antelope

moving

with

constant

acceleration

covers

the

distance

between

two

points

70

mapart

in

7

s.

Its

speed

as

it

passes

the

second

point

is

15

m/s.

(a)

What

is

the

speed

at

thefirst

point?

(b)

What

is

the

acceleration?

15

t

xxv

xave

0)(

2

0)(

xx

xave

vv

v

t

vva

xx

x

0

tavvxxx

0

1

tvv

xx xx

2

0

0 2

)(2 02

0

2xxavv

xxx 3

200

2

1tatvxx

xx 4

16

Example: A motorcyclist w/ constant acceleration.

a. What is his position and velocity after 2s?

b. Where is he when his velocity is 25m/s?

Solution:

2

00

2

1a. tatvxx

xx

2

2 )s2(

s

m4

2

1)s2(

s

m15m5

m43x

tavvxxx

0

)s2(s

m

4s

m

15 2

s

m23

xv

)(2b. 02

0

2xxavv

xxx

x

xx

a

vv

xx

2

2

0

2

0

2

22

s

m42

s

m15

s

m25

m5

m55x


5/7

17

Example: Two bodies with different acceleration.

a. How much time elapses before the officercatches up with the motorist?

b. What is the officers speed at that point?

c. What is the total distance each vehicle hastravelled at that point?

Solution:

2

00

2

1a. tatvxx

xx

18

Example: Two bodies with different acceleration.

a. How much time elapses before the officercatches up with the motorist?

b. What is the officers speed at that point?

c. What is the total distance each vehicle hastravelled at that point?

Solution:

tavvPxxPPx

0

b.

)s10(s

m3m0

2

s

m30

Pxv

c.

19

-> motion with constant acceleration

-> acceleration due to gravity (g=9.8m/s2) (regardless of mass)

-> acceleration is always directed downwards (ay = -g)

jgay )(

jvv yy )(

)(-jgay

jvv yy

20

-> motion with constant acceleration

-> acceleration due to gravity (g=9.8m/s2) (regardless of mass)

-> acceleration is always directed downwards (ay = -g)

tavvxxx

0

tvv

xx xx

2

0

0

)(2 02

0

2xxavv

xxx

2

002

1

tatvxx xx

gtvvyy

0

tvv

yy yy

2

0

0

)(20

2

0

2yygvv

yy

2

002

1gttvyy y


6/7

21

Example: A ball is dropped from the top of a building and starts to fall freely. Compute its positionand velocity after 1s, 2s and 3s

Solution:

-y

2

00

2

1gttvyy

y

at t=1s

2

2 (1s)

s

m9.8

2

10m0m

m9.4y

gtvvyy

0

)s1(sm8.9m02

s

m8.9

yv

at t=2s

m6.19y

s

m6.19

yv

at t=3s

m1.44y

s

m4.29

yv

t=1s

t=2s

t=3s

22

Example: A ball thrown upward and falling freely

15m/s

-y

+y

Find:

a. the position and velocity of the ball 1s and 4s after leaving yourhand

b. the velocity when the ball is 5m above the railingc. the maximum height reached by the ball and the time to

reach it

d. The acceleration at the maximum height

23

-y

+y

a. Find the position and velocity of the ball 1s and 4s after leavingyour hand

2

00

2

1gttvyy

y

at t=1s

2

2 )s1(

s

m8.9

2

1)s1(

s

m15m0

m1.10y

gtvvyy 0

)s1(s

m8.9

s

m15

2

s

m2.5

yv

at t=4s

m4.18

y

s

m2.24

yv

t=1s

t=4s

Solution:

24

b. Find the velocity when the ball is 5m above the railing

)(20

2

0

2yygvv

yy

wheny=5m

)(2 02

0 yygvv

yy

)m0m5(s

m8.92

s

m15

2

2

s

m3.11

yv

5m

+ySolution:


7/7

25

c. Find the maximum height reached by the ball and the time toreach it

d. The acceleration at the maximum height

)(2c. 02

0

2yygvv

yy

v = 0

Solution:

gyv y 2s

m

0

2

02

2

g

vy

y

2

2

0

2

2

s

m8.92

s

m15

m5.11y

gtvv yy 0

g

vt y0

2s

m8.9

s

m15

s53.1t

2s

m8.9d. ga

y

26

1. A subway train starts from rest at a station and accelerates at a rate of1.60m/s2 for14s. Itruns at a constant speed for 70s and slows down at a rate of 3.50m/s2 until it stops at thenext station. Find the total distance covered by the train.

2. Large cockroaches can run as fast as1.50m/s in short bursts. Supposeyou turn on the light in acheap motel and see one scurrying directly away fromyou at a constant speed of1.50m/s. Ifyoustart0. 90m behind the cockroach with an initial speed of0. 80m/s toward it, what minimumconstant acceleration wouldyou need to catch up with it when it has travelled1.20m?

3. A 15-kg rock is dropped from rest on the earth and reaches the ground in 1.75s. When it isdropped from the same height on Saturns moon Enceladus, it reaches the ground in18. 6s.What is the acceleration due to gravity on Enceladus?

4. A student throws a water balloon vertically downward from the top of a building. The balloonleaves the throwers hand with a speed of6.00m/s. Air resistance may be ignored so the balloonis in free fall after it leaves the throwers hand. (a) What is its speed after falling2.00s?(b) How far does it fall in2.00s? (c) What is the magnitude of its velocity after falling10.0m?(d) Sketch they-t, vy-t, ay-tgraphs for the motion.

phys10-chap2-1dmotion

Documents