One Dimensional Motion
description
Transcript of One Dimensional Motion
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
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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
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0 2 4 6 8
Time (s)
Dis
tan
ce (
m)
Distance
Distance vs Time GraphDictance vs Time
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0 1 2 3 4 5 6
Time (s)
Dis
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m)
Dictance
Displacement vs Time
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0 10 20 30 40 50 60 70 80
Time (s)
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pla
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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
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Time (s)
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(m)
Displacement vs Time
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Time (s)
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(m)
Displacement vs Time
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Time (s)
Dis
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Velocity vs Time Graphs
Velocity vs Time
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Ve
loc
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(m/s
)
a = sloped = xy or vtd = area
Velocity vs Time
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0 1 2 3 4 5 6 7 8 9 10Time (s)
Ve
loc
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(m/s
) a = slope = y/x = v/t = 62/5 = 12.4 m/s
Velocity vs Time
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0 1 2 3 4 5 6 7 8 9 10Time (s)
Ve
loc
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(m/s
) d = area under curve
Define each of the following
•DistanceDisplacement
•Speed Velocity
•Acceleration
Displacement vs Time
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Time (s)
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D
Describe the motion for each series
Displacement vs Time
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Time (s)
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pla
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Displacement
Describe the motion between each interval
Displacement vs Time
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0 1 2 3 4 5 6
Time (s)
Dis
pla
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t (m
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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
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Velocity vs Time
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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.
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Dis
plac
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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.
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