Post on 25-Dec-2015
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