Name:
Seat Letter&Number:
PHYS161 Fall 2021 EXAM 1
I pledge on my honor that I have not received or given any unauthorized
assistance on any part of this examination in its whole duration.
Signature _______________________________
• After the exam starts please don’t talk or look around. Try to avoid
situations which may be conjured as attempts to engage in dishonest
activities during exams. Academic integrity is taken seriously by the
University.
• Please print and sign your name above. Print your seat letter and
number. Do not turn this page until you are instructed to start.
• When the proctor tells you to begin, print your full name at the top of every
page. This is essential since this exam booklet will be separated for
grading. There will be a deduction from your score for every page without
a name.
• You may have one sheet of paper for equations and a calculator. Please
switch off your cell phone and place all materials directly underneath
your seat, not on the floor or in the seats next to you.
• Do your work for each problem on the page for that problem. You might
find it convenient to do your scratch work on the back of the page before
starting to write out your answer or to continue your answer on the back.
If part of your answer is on the back, be sure to check the box on the bottom
of the page so the grader knows to look for it!
• No points are given if only an answer is given, unless explicitly requested.
Show your work.
• If you run out of time on a problem, indicate the strategy you would have
taken to approach the problem, you may get partial credits for it.
_____________________________________________________________
Acceleration (m/s/s)
PHYS161 Fall 2021
Name:
5
4
3
2
1
0
-1 0
-2
-3
-4
-5
5
10
15
20
Time (s)
1. A student is asked to test a new accelerometer. She stands in an elevator and records
the acceleration reading as a function of time. The data are shown in the graph above
(the vertical axis has units of m/s2). At time t = 0, the elevator is at displacement x = 0
with velocity v = 0. Assume that the positive directions for displacement, velocity,
and acceleration are upward.
a. Determine the velocity v of the elevator for each 5-second interval.
i. Indicate your results by completing the following table.
Time (s)
v (m/s)
5
10
15
20
____
____
____
____
ii. Plot the velocity as a function of time on the following graph.
25
20
Velocity (m/s)
15
10
5
0
-5 0
Time (s)
5
10
15
20
-10
-15
-20
-25
2
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PHYS161 Fall 2021
Name:
b. Determine the displacement x of the elevator above the starting point for each 5second interval.
i. Indicate your results by completing the following table.
Time (s)
x (m)
5
10
15
20
____
____
____
____
Displacement (m)
ii. Plot the displacement as a function of time on the following graph.
250
200
150
100
50
0
3
0
5
10
15
Time (s)
20
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PHYS161 Fall 2021
Name:
2. A particle is constrained to move with a velocity in time using the following function:
v (t ) = (4t 2 + 2t − 5)i + (−2t 2 + 6) j + (t 3 − 2t 2 − 2)k
a. What is the equation of acceleration as a function of time?
b. If the object started at r(0) = (i + 2j – k) meters from the origin, find it position as
a function of time.
c. Calculate the distance from the origin, the speed, and magnitude of acceleration at
time t = 1 second.
d. At what time(s) does the particle stop in the i direction? What are the position, velocity, and acceleration vectors then?
4
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PHYS161 Fall 2021
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3. A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft
to the blade tip. The model is rotated in a wind tunnel at 550. Rev/min.
a. What is the linear speed of the blade tip in m/s?
b. What is the radial acceleration of the blade tip?
5
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PHYS161 Fall 2021
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4. Your friend’s car is parked on a cliff overlooking the ocean on an incline that makes
an angle of 17.0° below the horizontal. The brakes fail, and the car rolls from rest
down the incline for a distance of 29.0 meters to the edge of the cliff, which is 55.0
meters above the ocean, and, unfortunately, continues over the edge and lands in the
ocean.
a.
b.
6
Find the car’s position relative to the base of the cliff when it lands in the ocean.
Find the length of time the car is in the air.
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