While driving on the interstate, you notice your
speedometer is not working. To determine the
speed of your car, you use your watch to
measure the elapse time between each mile
marker. If the elapse time is 50 seconds, what is
your average speed in units of miles per hour?
Since the times are measured over an interval
of a 1 mile, the distance = 1 mile
The measured elapse time = 50 seconds, but the units must
be converted to hours
3600 sec = 1 hr, 1 = 1hr / 3600sec
Elapse time = 50sec = 50 sec x (1hr / 3600sec) = 50 / 3600 hour = 1 / 72 hr
Average speed = distance / elapsed time
= 1 mile / (1 / 72 hour) = 72mph
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Clicker
Cruising Along I
You drive for 30 minutes at 30 mi/hr
a) more than 40 mi/hr
and then for another 30 minutes at
b) equal to 40 mi/hr
50 mi/hr. What is your average
speed for the whole trip?
c) less than 40 mi/hr
Cruising Along I
You drive for 30 minutes at 30 mi/hr
a) more than 40 mi/hr
and then for another 30 minutes at
b) equal to 40 mi/hr
50 mi/hr. What is your average
c) less than 40 mi/hr
speed for the whole trip?
It is 40 mi/hr in this case. Because the average speed is distance/time
and you spend the same amount of time at each speed, then your
average speed would indeed be 40 mi/hr.
Average speed = distance / elapsed time
A car is driven over 4 miles at 30.0 mi/hour and then another 4.00 mi at 50.0
mi/hour. What is the average speed for 8.00 mile trip?
We want to first determine the elapse times t1 and t2 during the 4 miles segments
elapsed time= distance / Average speed
t1=4 miles / 30mph
t2=4 miles / 50mph
The total elapse time required to traverse the full 8 mile distance is the sum of t1 and t2
Average speed = distance / elapsed time = 8 miles / (t1+t2)=8/(4/30+4/50)= 37.5mph
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Clicker
Cruising Along II
You drive 4 miles at 30 mi/hr and
a) more than 40 mi/hr
then another 4 miles at 50 mi/hr.
b) equal to 40 mi/hr
What is your average speed for
c) less than 40 mi/hr
the whole 8-mile trip?
Cruising Along II
You drive 4 miles at 30 mi/hr and
a) more than 40 mi/hr
then another 4 miles at 50 mi/hr.
b) equal to 40 mi/hr
What is your average speed for
c) less than 40 mi/hr
the whole 8-mile trip?
It is not 40 mi/hr! Remember that the average speed is distance/time.
Because it takes longer to cover 4 miles at the slower speed, you are
actually moving at 30 mi/hr for a longer period of time! Therefore, your
average speed is closer to 30 mi/hr than it is to 50 mi/hr.
Acceleration is the rate change of velocity wrt time
Velocity is the rate change of displacement wrt time
•Given the position-time graph
•The velocity-time graph (b) is found
by measuring the slope of the
position-time graph at every instant
•The acceleration-time graph (c) is
found by measuring the slope of the
velocity-time graph at every instant
Acceleration and Velocity,
Directions
•When an object’s velocity and acceleration are in the
same direction, the object is speeding up.
•When an object’s velocity and acceleration are in the
opposite direction, the object is slowing down.
Motion Diagrams
•Red arrows represent velocity.
•Purple arrows represent acceleration.
Clicker
A. The velocity is decreasing
with time
B. The velocity is increasing
with time
C. It moves with a constant
velocity
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Clicker
A. The velocity is decreasing
with time
B. The velocity is increasing
with time
C. It moves with a constant
velocity
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Constant acceleration
expand
Multiply both sides by a
Combine
terms
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When acceleration is constant, the
velocity varies linearly with time.
As a result the average velocity is
simply the average of the initial
velocity and the final velocity
Must know final velocity
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Motion with Constant Acceleration
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Free Fall
In a vacuum, all bodies fall with the
same constant acceleration
Mechanical Universe
Free Fall Motion
http://www.learner.org/resources/series42.html
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