Transcript Wednesday 5/20 - University of Utah

Wednesday 5/20
PHYS 2010
Nathalie Hoffmann
University of Utah
Distance vs. Displacement
• What differences are there?
Distance vs. Displacement
• What differences are there?
• Distance: scalar
• Displacement: vector
• Distance: always positive
• Displacement: has direction (1D: plus/minus, 2D: angle w.r.t. x/y axis, etc.)
Speed vs. Velocity
• Differences?
Speed vs. Velocity
• Differences?
• Speed: scalar (always positive)
• Velocity: vector (i.e. has direction)
• Speed = distance/time (interval)
• Velocity = displacement/time (interval)
• NOTE: average speed does not necessarily equal magnitude of velocity
Acceleration
• What does it mean for an object to be accelerated?
• Examples
• Acceleration does not necessitate speeding up
Kinematics Equations (constant acceleration)
More Vector Problems
• The drawing shows a force vector that has a
magnitude of 475 Newtons. Find the (a) x, (b) y,
and (c) z components of the vector.
• What are the x and y components of the vector
that must be added to the following three
vectors, so that the sum of the four vectors is
zero? Due east is the +x direction, and due north
is the +y direction.
Kinematics Problems
• For each of the three pairs of positions listed in the following table,
determine the magnitude and direction (positive or negative) of the
displacement.
Initial position
Final position
(a) + 2.0 m
+ 6.0 m
(b) + 6.0 m
+ 2.0 m
(c) - 3.0 m
+ 7.0 m
• Now, suppose the data in the above table describe the initial and final
positions of a moving car. The elapsed time for each of the three pairs
of positions listed in the table is 0.50 s. Determine the average
velocity (magnitude and direction) for each of the three pairs. Note
that the algebraic sign of your answers will convey the direction.
More Problems
• The Olympic record for the marathon set in 2008 is 2 h, 6 min,32
s. The marathon distance is 26.2 mi. What was the average speed of
the record-setting runner in km/h? (1 mile = 1.609 km)
• A car traveling 80.0 km/h is 1500 m behind a truck traveling at 70.0
km/h. How long will it take the car to catch up with the truck?
• Alcohol consumption slows people’s reaction times. In a controlled
government test, it takes a certain driver 0.320 s to hit the brakes in a
crisis when unimpaired and 1.00 s when drunk. When the car is
initially traveling at 90.0 km/h, how much farther does the car travel
before coming to a stop when the person is drunk compared to
sober?
More Problems
• A runner starts from rest and achieves a maximum speed of 8.97
m/s. If her acceleration is 9.77 m /s2, how long does it take her to
reach that speed?
• In reaching her destination, a backpacker walks with an average
velocity of 1.34 m/s, due west. This average velocity results because
she hikes for 6.44 km with an average velocity of 2.68 m/s, due west,
turns around, and hikes with an average velocity of 0.447 m/s, due
east. How far east did she walk?
More Problems
• A car is traveling at 20.0 m/s, and the driver sees a traffic light turn
red. After 0.530 s (the reaction time), the driver applies the brakes,
and the car decelerates at 7.00 m/s2. What is the stopping distance of
the car, as measured from the point where the driver first sees the
red light?
• A jogger accelerates from rest to 3.0 m/s in 2.0 s. A car accelerates
from 38.0 m/s to 41.0 m/s also in 2.0 s.
• (a) Find the acceleration (magnitude only) of the jogger.
• (b) Determine the acceleration (magnitude only) of the car.
• (c) Does the car travel farther than the jogger during the 2.0 s? If so, how
much farther?