One Dimensional

Motion

Distance•How far

something has moved

Distance•Scalar quantity

Displacement•How far something

is from its starting position

Displacement

•A vector quantity

Time•The interval between two occurrences

Uniform Motion•Equal displacement

occurs during successive equal

time intervals

Uniform Motion•Velocity is

constant during uniform motion

t (s) 0 1 2 3 4 5 6P (m) 0 1 2 3 4 5 6

Position (P) vs Time Chart (t)

Distance vs Time GraphDistance vs Time

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Time (s)

Dis

tan

ce (

m)

Distance

Slope•Slope = rise/run

•Slope = y/x

Slope•On a distance vs time graph:

•Slope = d/t

Slope•Slope = d/t

•Slope = velocity

Average Velocity•v = d/t

•v = d1 – d0

t1 – t0

Displacement

•d1 = d0 + vt1

•d = d0 + vt

t (s) 0 1 2 3 4 5 6P (m) 0 2 8 16 36 44 48

Position (P) vs Time Chart (t)

Distance vs Time GraphDistance vs Time

0

10

20

30

40

50

60

0 2 4 6 8

Time (s)

Dis

tan

ce (

m)

Distance

Distance vs Time GraphDictance vs Time

0

10

20

30

40

50

60

0 1 2 3 4 5 6

Time (s)

Dis

tan

ce (

m)

Dictance

Displacement vs Time

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60 70 80

Time (s)

Dis

pla

cem

en

t (m

)

Displacement

Accelerationa = v/t

a = v1 - v0

t1 - t0

Velocity

v = v0 + at

vf = vi + at

Displacement

d = d0 + v0t + ½ at2

Displacement

df =

di + vit + ½ at2

v2 = v0

2 + 2 a(d1 – d0)

v2 = v02 + 2ad

vf2 = vi

2 + 2ad

v = v0 + atd = d0 + v0t + ½ at2

v2 = v02 + 2ad

v = v0 + at

vf = vi + at

d =

d0 + v0t + ½ at2

df =

di + vit + ½ at2

df =

di + vit + ½ at2

d = vit + ½ at2

v2 = v02 + 2ad

vf2 = vi

2 + 2ad

ff = vi + at

d = vit + ½ at2

vf2 = vi

2+ 2ad

DrillA ball is dropped from

490 m. Calculate its:

vf & tair

Determining Instantaneous Velocity

1) Graph the d/t data

2) Draw tangent to point of interest

3) Determine slope of tangent

Displacement vs Time

0

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10

Time (s)

Dis

pla

ce

me

nt

(m)

Displacement vs Time

0

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10

Time (s)

Dis

pla

ce

me

nt

(m)

Displacement vs Time

0

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10

Time (s)

Dis

pla

ce

me

nt

(m)

Velocity vs Time Graphs

Velocity vs Time

0

5

10

15

20

25

30

0 2 4 6 8 10Time (s)

Ve

loc

ity

(m/s

)

a = sloped = xy or vtd = area

Velocity vs Time

0102030405060708090

100

0 1 2 3 4 5 6 7 8 9 10Time (s)

Ve

loc

ity

(m/s

) a = slope = y/x = v/t = 62/5 = 12.4 m/s

Velocity vs Time

0102030405060708090

100

0 1 2 3 4 5 6 7 8 9 10Time (s)

Ve

loc

ity

(m/s

) d = area under curve

Define each of the following

•DistanceDisplacement

•Speed Velocity

•Acceleration

Displacement vs Time

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30

Time (s)

Dis

pla

cem

en

t (m

)

A

B

C

D

Describe the motion for each series

Displacement vs Time

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60 70 80

Time (s)

Dis

pla

cem

en

t (m

)

Displacement

Describe the motion between each interval

Displacement vs Time

0

2

4

6

8

10

0 1 2 3 4 5 6

Time (s)

Dis

pla

cem

en

t (m

)

A

B

C

D

Describe the motion of each series

Draw a position time graph for a person who walks

uniformly from the positive side of the origin back thru

the origin to the negative side. Repeat for the negative side.

Make the following conversions:

a) 10 m/s to km/hrb) 72 mph to m/s

1.6 km/mile

Draw a position time graph of a person who walks one

block briskly, waits at a traffic light, walks the next

block slowly, waits at another light, then runs the

last block.

A car starts 200.0 m west of town, and moves at 15 m/s east.1) write its best equation2) where will the car be at 10 min3) When will the car be in town

A truck starts 400.0 m east of town, and moves at 12 m/s west Find the time & place where the car from the last problem & the truck will be at the same place

A car increases its velocity from 4.0 m/s to 36 m/s over 4.0 s.

1) Calculate the average acceleration

The same car slows from 36 m/s to 15 m/s

in 3.0 s. 1) Calculate the average

acceleration & dis

A car is coasting backwards at 3.0 m/s when its engine starts. After 2.5 s the car is going 4.5 m/s. 1) Calculate the average

acceleration & displacement

A car going 4.0 m/s accelerates at 3.0 m/s2

for 4.0 s. 1) Calculate its final

velocity & displacement

A car slows from 44 m/s to 22 m/s in 11 s.

Calculate its acceleration & displacement

A car accelerates from 15 m/s to 25 m/s in

125 m. 1) Calculate its time &

acceleration

A ball is dropped from a 0.49 km cliff. The

acceleration of gravity is -9.8 m/s2.

1) Calculate its time in air & final velocity

A ball is thrown straight up at 19.6 m/s. The

acceleration of gravity is -9.8 m/s2.

1) Calculate its time in air & maximum height

A man on the ground shoots a gun straight up & the bullet exits the barrel at

980 m/s. The acceleration of gravity is -9.8 m/s2.

Calculate its time in air, vf, & maximum height

A cannon on a 2500 m cliff is fired straight up & the

ball exits the barrel at 0.98 km/s. The acceleration of

gravity is -9.8 m/s2. Calculate its time in air, vf,

& maximum height

A ball is shot straight up to a height of 1.96 km. The acceleration

of gravity is -9.8 m/s2. 1) Calculate its time in

air & final velocity.

A ball was dropped & landed at 70.0 m/s. The

acceleration of gravity is -9.8 m/s2.

1) Calculate its height & time in air.

A pumpkin was dropped from a plane & stayed in

air for 10.0 s. The acceleration of gravity is

-9.81 m/s2. 1) Calculate its height &

final velocity.

A car increases its velocity from 36 km/hr

to 72 km/hr in 5.0 s. Calculate its acceleration & displacement during

that time.

A car rolling backwards at 5.0 m/s accelerates at 3.0

m/s2 for 4.0 s.Calculate its final velocity

& displacement during that time.

A car rolling backwards at 25.0 m/s accelerates at

5.0 m/s2 for 12.0 s.Calculate its final velocity

& displacement during that time.

A ball is thrown straight up at 9800 cm/s.

Calculate the maximum height of the ball & its

time in air.

A ball is thrown straight down at 25 m/s & stays

in air for 4.0 s. g = -9.8 m/s2

Calculate the initial height & vf of the ball.

A ball is thrown straight up to a height of 49 m.

g = -9.8 m/s2

Calculate the initial velocity & time in air.

A ball is thrown straight sideways & lands in

5.0 s. g = -9.8 m/s2

Calculate the final down velocity & height.

A car rolling backwards at 5.0 m/s accelerates to 11

m/s forward in 4.0 s.Calculate its acceleration

& displacement during that time.

A car going 36 km/hr slams on brakes, but still hits a tree at 6.0 km/hr

after 1.0 s. Calculate: its acceleration &

displacement during that time.

Displacement vs Time

-10

0

10

20

30

40

0 2 4 6 8 10

Time (s)

Dis

plac

emen

t (m

)

Velocity vs Time

-20

0

20

40

0 2 4 6 8 10

Time (s)

Vel

ocit

y (m

/s)

A ball is thrown straight up and hits the ground in

6. sec. Calculate the ball’s max height & max

velocity.

A car goes from 36 km/hr to 54 km/hr in 5.0 s.

Calculate: its acceleration &

displacement during that time.

40

30

20

10

0

-10

-20

-30

-401 2 3 4 5 6 7 8 9 10

Dis

plac

emen

t (m

)Displacement vs Time graph

A ball is thrown straight up at 49 m/s.

Calculate the time in air & the max height.

A car rolling backwards at 6.0 km/hr accelerates to 30.0 km/hr forward in

6.0 s.Calculate its acceleration

& displacement during that time.

5

4

3

2

1

0

-1

-2

-3

-4

-5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Vel

ocit

y (m

/s)

Time (s)