practice
- Complete the worksheet on the first page of worksheet-compare.pdf.
Fill each grid space with an appropriately concise answer.
- Work along with this example using worksheet-transform.pdf.
The graph below shows velocity as a function of time for some unknown object.
- What can we say about the motion of this object?
- Plot the corresponding graphs of displacement and acceleration as functions of time.
- Sketch the displacement-time, velocity-time, and acceleration-time graphs for …
- an object moving with constant velocity. (Let the initial displacement be zero.)
- an object moving with constant acceleration. (Let the initial displacement and velocity be zero.)
- The graph below shows the acceleration of a hydraulic elevator in a four
story school building as a function of time.
The graph begins at t = 0 s when the elevator door
closed on the second floor and ends at t = 20 s when
the door opened on a different floor. Assume that the positive directions
for displacement, velocity, and acceleration are upward. Determine …
- the maximum speed of the elevator
- the duration of the brief jerk experienced by the elevator centered on 17.5 s
Sketch the corresponding graphs of …
- velocity-time
- displacement-time
Determine …
- the most likely floor on which the elevator stopped
worksheets
- worksheet-graph-displace.pdf
The worksheet for this exercise consists of three small and one large displacement-time graph.
- Complete the three small displacement-time graphs from the information
provided below each graph.
- The larger displacement-time graph shows the motion of some hypothetical
object over time. Break the graph up into segments and describe qualitatively
the motion of the object in each segment. Whenever possible, calculate the
velocity of the object as well.
- worksheet-graph-velocity.pdf
The worksheet for this exercise consists of three small and one large velocity-time graph.
- Complete the three small velocity-time graphs from the information provided
below each graph.
- The larger velocity-time graph shows the motion of some hypothetical object
over time. Break the graph up into segments and describe qualitatively the
motion of the object in each segment. Whenever possible, calculate the acceleration
of the object as well.
- worksheet-choose-displace.pdf
The graphs on the accompanying pdf show the displacement of a hypothetical object
moving along a straight line. Choose the lettered graph that best represents
each of the numbered descriptions. A graph may be used for more than one description
or it may not be used at all. Some descriptions may correspond to more than one
graph and some may not correspond to any graph at all.
- worksheet-choose-velocity.pdf
The graphs on the accompanying pdf show the velocity of a hypothetical object
moving along a straight line. Choose the lettered graph that best represents
each of the numbered descriptions. A graph may be used for more than one description
or it may not be used at all. Some descriptions may correspond to more than one
graph and some may not correspond to any graph at all.
conceptual
- conceptual.pdf
Sketch the displacement-time, velocity-time, and acceleration-time graphs for
each of the following scenarios. (Be prepared to explain your sketches.)
- An elevator that ascends from the lobby to the 36th floor, stops, descends
to the 27th floor, stops, and returns to the lobby.
- A basketball is dropped on the court and allowed to bounce up and down
several times undisturbed.
- A car on a test track performing a zero-to-sixty acceleration test. (This
acceleration will not be uniform.)
- A race between a tortoise and a hare that unfolds just like the fable of
the same name. (An acceleration-time graph is not necessary for this
particular problem.)
- Two cars are adjacent to each other on a four-lane highway. The first car
accelerates uniformly from rest the moment the light changes to green. The
second car approaches the intersection already moving and is beside the first
car at the instant the light changes. It then continues driving with a constant
velocity.
- Traffic lights on some streets are timed to facilitate traffic flow at
a certain speed. Goofus and Gallant are stopped at a red light on this kind
of street. When the light changes Goofus hammers the accelerator until he
exceeds the speed limit. He arrives at the first light which is still red
and stops. Gallant accelerates at a reasonable rate and never exceeds the
speed limit. The second light turns green at just the right instant so that
he never needs to brake at an intersection. Goofus and Gallant continue driving
this way for three lights.
numerical
- The graph to the right
shows the altitude of a skydiver initially at rest as a function of time. After
7 s of free fall the skydiver's chute deployed completely, which changed
the motion abruptly.
- Determine the velocity at the instant …
- just before the parachute opened.
- just after the parachute opened.
- What was the skydiver's acceleration …
- from the beginning of the jump to the time just before the parachute
opened?
- from the time just after the parachute opened to the time when the
skydiver landed?
- Sketch the corresponding graphs of …
- velocity-time.
- acceleration-time.
- The graph to the right
shows the velocity of a skydiver as a function of time. At time t = 0 s
the skydiver is located at position y = 0 m at the door
of the plane, at t = 8 s the parachute opened, and at t = 12 s
the skydiver touched down. Assume that the positive directions for displacement,
velocity, and acceleration are downward. Using this information sketch the corresponding
graphs of …
- displacement-time.
- acceleration-time
statistical
- special-splits.html
A split is a time at which the runner reaches a
milestone distance in a race. In the 100 m dash, for example, split times
are taken every 10 m. Splits for some of the world's fastest sprinters are
given on the accompanying webpage. Fit a high order polynomial (fourth, fifth,
sixth or higher) to the data for one of these athletes using a data analysis
application. Determine the speed of your sprinter as a function of time by taking
the derivative of this polynomial. Graph this new function and then analyze it.
- What were the runner's initial and final speeds?
- What was the runner's maximum speed and when did it occur?
- What was the runner's average speed?
- Did the runner's speed increase, decrease, or remain roughly the same near the end of the race?
- How well do you think this graph describes the actual performance of the runner? Are there any problem regions on the graph? How could the function be modified to improve the fit?
- jet-takeoff.txt, jet-landing.txt
One fine day, a Boeing 717 departed from Mitchell International Airport
(MKE) in Milwaukee. Approximately two hours later, it arrived at Laguardia Airport
(LGA) in New York. During takeoff and landing,
runway positions (in meters) were recorded as a function of time (in seconds)
and the data were saved as tab-delimited text files. Using the data in these
files and your favorite graphing software …
- construct a graph of distance vs. time for…
- takeoff and
- landing
- then add an appropriate curve fit so that you can determine …
- the acceleration at takeoff and
- the deceleration on landing
- and also determine …
- the final speed when the airplane left the runway in Milwaukee and
- the initital speed when the airplane hit the runway in New York
investigative
- The numbered streets in Manhattan above 14th Street are spaced apart such that
twenty blocks equal one mile. Ride one of the local trains that runs beneath
an avenue for at least five consecutive stations. Using a timer or a wristwatch
record the starting and stopping times of the train and the street number of
the station until you have reached the fifth station. Translate your data into
a displacement-time and velocity-time graph. Include the necessary data tables.
Use whatever units you wish. (This investigation can also be performed in other
places in a car or a bus if the streets are gridded and you know the grid interval.)