physics 534 chapter 9
TRANSCRIPT
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Chapter 9
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Uniform Motion
The simplest motion is straight line motion in a specific direction at a constant speed.
When both speed and direction remain thesame, it is called uniform motion.
Speed is a scalar quantity, = distance/time.
Velocity is the vector quantity denoting speed and direction.
Velocity is the displacement of an objectper unit of time.
V = d/t, d - displacement, t ± time
interval.
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Random Motion
The motion of these particles are random
because their speed and direction change.
This is an example of the KineticMolecular Theory (Chemistry).
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Graphing Distance-Time
Time is independent and on the x-axis.
Distance depends on time and is on the y-
axis. The slope of the graph gives us the speed.
If it was a displacement-time graph, slope
would give the velocity.
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Graphing Displacement
Velocity is considered to be dependent on
time.
Average velocity = total displacementtotal time
av = d/t
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Calculating Speed
Average speed = total distance
total time
av = dtotal/t
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Activity
Page 194, Q. 1-3
Page 196, Q. 1-3
Investigation, Page 196 Lab: Uniform Motion
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Activity
Page 199, Q. 1,4
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Velocity at a Point
This is done by taking the slope of a line
that touches at the specific time.
See page 207 for examples.
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Activity
Page 203, Q. 1-4
Page 208, Q. 1-4
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Average Velocity
Average Velocity is defined as the change
in displacement over time.
av = d/ t Average Speed is the change in distance
over time.
av = d/ t or under uniform acceleration = v2 + v1
2
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Pr o jectile Motion
Pr o jectile Motion
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Distance f r om Speed
We already know that speed = distance
time
So distance = speed x time Distance can be determined by the area
under the curve of a velocity-time graph.
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Acceleration
Acceleration is the change in velocity with time.
Acceleration = change in velocity
time interval
a = v = v2 ± v1
t t
a is the acceleration, m/s/s = m/s2
v2 is the final velocity, m/s v1 is the initial velocity, m/s
A negative acceleration = a deceleration
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Getting Info f r om a Graph
Fr om a graph of velocity-time, the distance
is the area under the graph.
Fr om a graph of velocity-time, theacceleration is f r om the slope.
Fr om a graph of acceleration-time, the
velocity is the area under the graph.
Page 213, Q. 1
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Activity
A car accelerates f r om 0 to 100 km/h in 10s.
What is the acceleration, in m/s2?
a = v = v2 ± v1 = 100 km/h ± 0 km/h
t t 10s
= 10 km/h/s
10 km x 1 hr x 1000m = 2.78 m/s2
hr 3600s km
Do page 215, Q. 1-3, page 217, Q. 1,2
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Final Velocity
Velocity can be calculated if we consider it
in terms of the initial velocity which has
under gone acceleration or deceleration.
v = u + at
v = final velocity, in m/s
u = initial velocity, in m/s a = acceleration, in m/s2
t = time of acceleration, in seconds
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Activity
What is the final velocity of a person
walking at 4 m/s who accelerates at 1 m/s2
for 5 s?
v = u + at
= 4m/s + 1m/s2 x 5s
= 4m/s + 5m/s = 9m/s
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Distance Covered
Distance can be determined if the initial
velocity, time and acceleration are known.
s = ut + ½ at2
s = distance, m
u = initial velocity, m/s
t = time, seconds a = acceleration m/s2
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Activity
What is the depth of a well, if when you
dr op a r ock, it takes 5 seconds to hit the
bottom?
s = ut + ½ at2
= 0(5) + ½ (9.81m/s2)(5s)2
= 0 + ½ (9.81)(25) = 122.625 m
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Hor izontal vs Vertical Motion
ONLY in situations where objects aremoving vertically thr ough space, theacceleration is 9.81 m/s2.
An object dr opped has an initial velocity of 0 m/s.
The acceleration due to gravity slows
objects moving upwards and speeds upobjects moving downwards.
Do page 221, Q. 1-4, p. 225, Q. 1-4
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Short Cut
What is the final velocity of a car if it starts
at 10 m/s and accelerates at 2 m/s2 over a
distance of 100m?
v2 = u2 + 2as
= (10 m/s)2 + 2(2m/s2)(100m)
= 100 + 400 v2 = 500
v = 22.4 m/s
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Exam Question
A motorcyclist, travelling at a speed of 30 m/s, sees an obstacle 100 metres in front of him and
puts on the brakes. He hits it 5.0 seconds later.
If the motorcycle slows down uniformly, how fast was it going at the instant of the collision?
A) 10.0 m/s
B) 8.0 m/s
C) 6.0 m/s
D) 4.0 m/s
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Exam Question
From t top of a tower an object i t rown verticall downward wit a velocit of 20 m/
What i the velocit of the object af ter it has fallen 60 metres?
A) 55 m/s
B) 50 m/s
C) 45 m/s
D) 40 m/s
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Summary
When air resistance is negligible, all f reelyf alling objects have the same downwardacceleration.
A ball r olling down an incline has uniformacceleration.
Acceleration due to gravity has a value of
9.81 m/s2
. Equations der ived for uniform acceleration
apply to f reely f alling objects.
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Summary
A negative slope on a straight line position-time graph indicates motion in a negative
direction at constant velocity.
Average velocity = displacement/time intervalwhich can be taken at any 2 times on a
position-time graph.
Average speed = total distance/time interval Instantaneous velocity can be taken f r om the
slope of the tangent to the curve at that time.
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Summary
Velocity is a vector quantity which may befound if the velocity is uniform, withvelocity = displacement/time.
Speed is a scalar quantity which may befound, if the speed is uniform, withspeed = distance/time.
The position-time graph for an objectmoving with uniform motion is a straightline. The slope of the straight line givesthe velocity.
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Summary
Acceleration is the rate of change of
velocity over time.
a = /t = (2- 1)/t On velocity-time graphs, a straight line
shows that an object has a constant
acceleration.
On a velocity-time graph, the acceleration
is the slope of the line.
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Summary
A negative slope on a velocity-time graphmeans that the magnitude of the velocity is
decreasing, if the object is moving in a
positive direction.
The area under the velocity-time graph
gives the displacement.
v = u + at
s = ut + ½ at2
v2= u2 + 2as
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Summary
If the motion is in a straight line, the vector
notation may be omitted and +/- signs
used instead.
A curved velocity-time graph indicates a
changing acceleration. The average
acceleration for an interval is found by
finding the slope between two points on the graph.
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Summary
The acceleration at any point on a curved
velocity-time graph is the slope of the tangent to
the curve at that point.
To construct a velocity-time graph f r om a ticker tape recording, mark the tape into lengths of the
same time interval. The displacement for each
interval divided by the time gives the average
velocity for that interval. Plotting the averagevelocity for each interval versus the time will
yield a velocity-time graph.
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Exam Question
A diver jumps from a height of 3.0 metres above the height of the water and touches the surface
1.0 s later.
What was his velocity when he hit the water?
A) 8.0 m/s
B) 7.0 m/sC) 6.0 m/s
D) 5.0 m/s
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Activity
Page 242, Q. 16-19, 22, 23,
27, 40, 46, 50, 51, 56, 58