One Dimensional Motion

AP Physics C

Terms

Displacement vs. Distance

Displacement: Change in position (vector)

• Distance: How far an object has travelled (scalar)

• Symbol: Δx or Δx

• SI Unit: meter, m

Position

f ix x x

Terms

Velocity vs. Speed

• Velocity: Rate of the change in position (vector)

• Speed: Rate of distance covered (scalar)

• Symbol: v or v

• SI Unit: meter per second, m/s

Average Velocity

xv

t

Instantaneous Velocity

xdt

dxvinst

Terms

Acceleration vs. Acceleration

• Acceleration: The rate at which velocity changes (vector)

• Acceleration: The rate at which speed changes (scalar)

• Symbol: a or a

• SI Unit: meters per second per second or meters per second squared, m/s/s or m/s2

Average Acceleration

va

t

Instantaneous Acceleration

xdt

xda

vdt

dva

inst

inst

2

2

Position vs. Time Graph

The slope of

an x vs. t

graph is the

velocity

What are the velocities?

rise 2 0(a) 2 /

run 1 0(b) 0 m/s

(c) 1 m/s

0 3 3(d) 1.5 /

5 3 2

xm s

t

m s

What are the velocities?

(a) -1m/s

(b) 2 m/s

(c) -0.5 m/s

Average Velocity on an x-t graph

vav vs vinst on an x-t graph

x-t graph vs motion of a particle

Instantaneous Velocity on an x-t graph

Velocity vs. Time Graph

• The slope of a v vs. t graph is the acceleration

• The area between the curve and the horizontal axis of a v vs. t graph is the displacement

Comparison of v-t to a-t graphs

Instantaneous Acceleration vs Average Acceleration from a v-t graph

v-t graph vs motion of a particle

x-t graph vs motion of a particle with acceleration

What are the accelerations and displacements?

2(A) a=2 m/s

1x=

2(.5)(5)(10) 25

bh

m

(B) a=0

x = LW

(10)(10) 100m

2(C) 0.5 /

1

2(5 10) (.5 10 5) 75

a m s

x LW bh

x x x m

What are the accelerations and displacements?

2

2

2

(A) 0.2 /

10

(B) 0.8 /

x=20

(C) 0.4 /

40

a m s

x m

a m s

m

a m s

x m

Acceleration vs. Time Graph

• The slope means NOTHING

• The area between the curve and the horizontal axis is the change in velocity

a

t-10 m/s/s

10 s

100 /v m s

Important

Acceleration tells us how fast velocity changes

Velocity tells us how fast position changes

Kinematics Equations(accelerated motion)

sderivationfor board See2

1

2

20

20

2

0

attvx

xavv

atvv

Falling Bodies, thrown up objects, and the y-direction

• All things fall at the same rate (neglecting air resistance)

• On earth that rate is 9.80 m/s2

• That rate is an acceleration

• The name of that acceleration is Gravity

Object moving in y-dir

Changing Acceleration

Velocity by Integration

2

1

2

1

v

v

t

tdtadv

dtadv

dtadvdt

dva

tdtavv

v

00

01

1

then...

v

0at t if

Position by Integration

2

1

2

1

x

x

t

tdtvdx

dtvdx

dtvdxdt

dxv

tdtvxx

x

00

01

1

then...

x

0at t if