Honors Physics Midterm Review Sheet
Fall, 2013, Wilmington High School
For your midterm exam, you should be able to do the following:
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Define displacement, velocity, and acceleration, as well as all terms from your
book readings
Define the kilogram, the meter, and the second according to the universally-agreed
measurement standards
Use the three fundamental quantities of length (L), mass (M), and time (T) to
derive expressions
Describe physical quantities in terms of being a vector or a scalar
Apply the concept and definition of displacement to both quantitative and
qualitative questions
Apply all of the equations from chapter 2, including the definitions of speed,
velocity, average velocity, acceleration, and all of the kinematics equations.
Derive ALL of the kinematics equations (as explicitly covered in class), and
rearrange all of the equations to solve real-world problems. You will be GIVEN the
fundamental equations, but you are expected to know how to rearrange them,
manipulate them, combine them, derive them, etc.
Use graphical and algebraic analysis to solve story problems pertaining to
kinematics
Distinguish average velocity from instantaneous velocity from a graphical
perspective
Apply the definition of a derivative to motion diagrams (Δx/t) in order to
formulate functions such as v(t) and a(t)
Explain acceleration in terms of velocity
Formulate velocity and acceleration equations given displacement as a function of
time. E.g. if the displacement of a particle as a function of time is given
according to the expression x(t) = 3t3 + t2 – 4t, derive expressions for v(t) and
a(t), and explain the relationship of the three functions in terms of their
graphical characteristics.
Analyze the free-fall motion of an object in terms of the relationship between the
object’s velocity and acceleration
Sample Math Problems
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During a football play, Nick moves 2.5m west, then moves 20.0m east, and then
moves west again for 45.0m. If east is chosen as the positive direction, what
was Nick’s resultant displacement? How much distance did he cover?
What is 3.441 x 2.00 x 1.0300 in the correct number of significant figures?
How many significant figures does each of the following numbers have
i. 2.0
ii. 2.0100
iii. 0.0002
iv. 0.002010
v. 10000
vi. 1000.001
vii. 23400
viii. 1.0010
ix. 4220002
In the hypothetical equation x = αvt3, where alpha is a constant, x is
displacement, v is velocity, and t is time, determine the dimensions of the
constant (alpha).
Suppose that a cylindrical oatmeal container has a diameter of 3.7 inches and a
height of 14.2 inches. Determine the volume of the container in a) in3, b) cm3,
and c)L
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The obnoxious-yet-mute Aflac duck, accelerating from rest at a constant rate,
experiences a displacement of 35m in 12 seconds. What was the average velocity
of that unbearably-annoying-yet-mute Aflac duck?
Suppose Mr. Farrell is diligently grading his quarter exams in the middle of an
open field when, all of the sudden, a caffeinated cheetah bursts onto the scene
and steals his answer key and coffee mug from his hands. Assume that Mr. Farrell
can run at approximately 120 km/hr after a few cups of coffee, and a cheetah can
run at 100 km/hr. If both Mr. Farrell and a cheetah are running at full speed,
with the cheetah 90.0m ahead of Mr. Farrell at some time t = 0 during his fullspeed pursuit, how long before Mr. Farrell catches the cheetah and reclaims his
rightful coffee mug and answer key?
The sun’s nearest neighbor star is roughly 4.5 light years away. How far away is
it in miles? USE SCIENTIFIC NOTATION!
If point A is located at (-5,2) and point B is located at (3,8), what is the
distance from point A to point B if the units of the coordinated system are
meters?
Give an order-of-magnitude estimate for the number of times Mr. Wilson has
blinked in his lifetime. Compare this to the order-of-magnitude estimate for the
number of times you’ve blinked in your lifetime.
In a far-away galaxy, the distance of a star named Quigsol from its orbiting
planet Probusville is 122,000,000,000 miles. Find the orbital speed the planet
Probusville in miles per second, assuming that it takes 750 Earth years to
complete one full revolution.
If a right triangle has a hypotenuse of 10.0 cm and one of its legs has a length
of 4.80cm, what is the length of the other leg? What is the angle measure
between the 4.80cm leg and the hypotenuse? What is the tangent of that angle?
Andrew boldly claims that his truck can accelerate at a constant rate, from rest
to 100km/hr, in just 5 seconds. If so, what is the acceleration of his truck in
m/s2? Please don’t test this!!!
i. Also, be able to convert the speed into m/s!
If Andrew’s truck COULD accelerate at the rate determined in question 13, what
total displacement could he cover (starting from rest) in 24.99 seconds?
A ball is pushed with an initial velocity of 3.0 m/s. The ball rolls down a hill
with a constant acceleration of 2.1 m/s2. The ball reaches the bottom of the hill
in 12.0s. What is the velocity of the ball at the bottom of the hill?
A “tricked out” school bus designed to operate on a drag strip accelerates from
zero to 30 m/s while undergoing a straight-line displacement of 100m. What is
the vehicle’s acceleration, assuming it is constant?
A “superpuma” starts from rest and accelerates at 8 m/s2 for a straight-line
distance of ¼ mile. What is the velocity of the superpuma (in m/s) at the ¼
mark?
While bored in the city, Teddy throws a ball straight upward off of a tall
building with an initial upward velocity of 75.0 miles per hour. If the ball
were released from a height of 650.0 feet above ground level,
a. Convert the velocity to m/s and convert the height to meters
b. How long will it take the ball to hit the ground?
c. What is the highest the ball gets relative to ground level?
d. How long does it take the ball to reach its maximal height?
e. At what time(s) is the ball 15.0 meters above its release point?
f. At what time is the ball 350 feet from ground level?
g. What is the velocity of the ball when it hits the ground?
If the displacement of an object is given in SI units by x(t) = -5t + 2t2, at t =
2 seconds:
i. What is the velocity of the object?
ii. What is the acceleration of the object?
iii. What is the displacement of the object?
 Also be able to use calculus to find v(t) and a(t) functions
given the x(t) function.
 Be able to sketch a graph of the x(t), v(t), and a(t) functions.
 Using the graphs, can you tell what time intervals have positive
velocity, negative velocity, or zero velocity? When does the
object change directions?
20)
If the displacement of an object is given by
x(t) = t3 – 5t2 + t – 9 ,
i. Find the displacement of the object at the following times
 t=0
 t=1
 t=3
 t=5
ii. Find the velocity of the object at the following times
 t=0
 t=1
 t=3
 t=5
b. Find the acceleration of the object at the following times
 t=0
 t=1
 t=3
 t=5
Even More Math Fun!!!
A rock is thrown straight downward off a cliff with an initial velocity of 10.0 m/s.
What is the rock’s displacement after 2.0s? Recall that the acceleration due to gravity
near Earth’s surface is (and always will be, in this class) approximately 9.8 m/s2.
A baseball is thrown straight upward with an initial velocity of 20.0 m/s. What is the
maximal height the baseball will reach before starting to fall downward? Once again, use
the gravitational acceleration constant given in question 10.
A golf ball is released from rest from the top of the Siuol Ts arch (like the St. Louis
arch, only totally made up and uncreatively named). It hits the ground after falling for
11.8s. What was the height from which the ball was dropped? Let the gravitational
constant in this fictitious problem be Earth’s gravitational constant, and assume air
resistance is negligible.
Mr.
box
the
hit
Reents releases a football (initially at rest) from the top of the Becker Field press
(20m above ground level). If g = 9.8 m/s2 and air resistance is negligible, what is
speed of the football as it hits the ground? How long will it take for the ball to
the ground?
At the edge of a cliff 200m high, Mr. Farrell is once again grading quarter tests. After
Joe scores a perfect 100% on his Pre-Calculus exam, Mr. Farrell celebrates by throwing
his spherically-shaped stainless steel coffee thermos straight upward with a velocity of
18 m/s. How much later would Mr. Farrell have to drop a super-sized sugar cube from rest
so that both the thermos and the sugar cube arrive simultaneously at the bottom of the
cliff? Neglect air resistance, and use g = 9.8 m/s2.
Assume that a mountain peak is found on the distant planet Probusville that towers
22,500m high. If g = 13.7 m/s2 on Probusville (it is much bigger than Earth, so it’s
gravitational acceleration is higher), how fast would a dropped object be moving if it
could free-fall to ground level after being released from the peak? Neglect air
resistance.
A bus leaves the WHS parking lot and accelerates at a constant rate for 5 seconds. During
this time, the bus traveled 40m. Then the bus traveled at a constant speed for 10
seconds. Then the driver spotted a crocodile crossing the road just 15m ahead and slammed
on the breaks. Assume the bus “decelerates” at a constant rate and comes to a stop just
in front of the crocodile. What was the initial acceleration of the bus? What was the
velocity of the bus after 5 seconds? What was the breaking acceleration of the bus? How
long did the bus brake? What was the total distance from the bus to the crocodile at the
beginning of the trip, assuming a straight line trip? Also be able to sketch a d vs. t, v
vs. t, and a vs. t graph for this situation.
The first 5.0 seconds of a remote control car’s motion can be modeled by the function
x(t) = 1.75t3 – 2t, where x is measured in feet.
a) What is the displacement of the car at t = 2 seconds?
b) Derive a velocity equation that gives the cars velocity as a function of time in
METERS PER SECOND
c) What is the car’s velocity at t = 2 seconds?
d) Derive an acceleration equation that gives the car’s acceleration as a function
of time.
e) What is the car’s acceleration at t = 2 seconds?
A blue ball is thrown upward with an initial speed of 20 m/s, from a height of 0.7 meters
above the ground. 2.4 seconds after the blue ball is thrown, a red ball is thrown down
with an initial speed of 9.7 m/s from a height of 22.6 meters above the ground.
a) Create a displacement vs. time graph for both balls (use the same graph and label
each)
b) Create a velocity vs. time graph for both balls (use the same graph and label each)
c) How long will it take each ball to hit the ground from when they were released?
The graph shown below gives the displacement vs. time for an object. Answer the questions
below:
a) What is the average velocity of the object from t = 0.5 to t = 1.25?
b) At what times does the particle have an instantaneous velocity of zero?
c) During what time interval(s) does the object have NEGATIVE instantaneous velocity?
(e.g. [x, y])
d) During what time intervals does the object have positive instantaneous velocity?
e) Describe the acceleration of the object from t = 0 to t = 0.06 seconds.
Knowing this review sheet should assure you a fairly good grade. However, this midterm
review sheet is not necessarily all-encompassing. To ensure a high grade on the midterm,
I strongly recommend that you study ALL worksheets, book problems, notes, worksheets,
book figures, graphical concepts, and equation derivations!!