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Two birds are flying directly towards each other at the same speed If the
first bird is flying at a velocity
v
, what is the the velocity of the
second bird?

(A)
v

(B)
- v

(C)
2v

(D)
Impossible to determine

A United Airlines jet is flying at 300 km/hr, while an Air France Concord is
speeding along at 1200 km/hr Both airplanes are flying at the same
altitude If each aircraft experiences problems with an unruly passenger,
and they both decide simultaneously to push the passenger out the door,
which of the unruly passengers will hit the earth first? (Ignore air
resistance)

(A)
The Air France passenger

(B)
The United Airlines passenger

(C)
Neither They will both hit the ground at the same time

(D)
Impossible to determine The answer depends on which passenger is heavier

Assuming the airplanes in the previous problem continue to travel at the
same velocity after ejecting their respective passengers, where will the
passengers land with respect to their aircraft's path?

(A)
When they hit the ground, they will be directly beneath the airplane they
fell from

(B)
When they hit the ground, they will be directly beneath the spot at which
the airplane threw them out

(C)
They will be in front of the aircraft they fell from

(D)
It depends on which plane the passenger fell from

The velocity function is all of the following EXCEPT

(A)
A function of time

(B)
The derivative of the position function

(C)
A function which gives the velocity of an object at any point in time

(D)
None of the above

A police officer living on a planet with no air resistance drops a pair of
handcuffs and a handkerchief from the same height at the same time Which
one will reach the ground first?

(A)
The handkerchief

(B)
The handcuffs

(C)
They will both hit the ground at the same time

(D)
The answer depends on how far above the ground they were when he dropped
them

What kind of function is an acceleration function describing one-dimensional
motion?

(A)
A scalar-valued function

(B)
A vector-valued function

(C)
There is no such thing as acceleration in one dimension

(D)
A constant function

In general, the acceleration of objects due to the earth's gravitational
pull is

(A)
constant

(B)
98
m/s
^{2}

(C)
smaller if the object is further away

(D)
greater if the object is further away

Kinematics is concerned with

(A)
understanding why objects move the way they do

(B)
describing the movement of objects

(C)
action at a distance

(D)
None of the above

A raindrop on a drizzly day takes one minute from the time it leaves the
cloud until it hits your umbrella, 3 miles below The average velocity of
the raindrop on its journey is

(A)
3 miles/hr

(B)
60 miles/hr

(C)
180 miles/hr

(D)
Impossible to determine because the raindrop accelerates due to gravity

The average velocity and the instantaneous velocity of an object will be the
same if

(A)
the object's speed is constant

(B)
the object's acceleration is zero

(C)
the object's velocity is always positive

(D)
They are never the same

A car traveling at constant velocity
v
suddenly brakes in an effort to
keep from hitting a rabbit which is 8 ft away If the braking action causes
a constant deceleration
a
, how long does it take for the car to come to a
complete stop?

(A)
t = va

(B)
t = 8a/v

(C)
t = 8a

(D)
t = v/a

In the previous question, how far did the car travel as it was braking?

(A)

(B)

(C)
8av

(D)
a^{2}

If the car from the last two questions had initially been traveling at a
speed of 10 ft/s, and experienced (from the braking) a deceleration of 5
ft/s
^{2}
, would it have hit the rabbit which was 8 ft away? (Assume the
rabbit was dazed and didn't move at all)

(A)
yes

(B)
no

(C)
Impossible to determine without knowing the weight of the car

(D)
Impossible to determine because the car can never reach a complete stop

Find the derivative of
2x^{5} +
x^{3} + + 5

(A)
10x^{5} + x^{2} + 5

(B)
10x^{4} + x^{2} -

(C)
10x^{4} + x^{2} + + 5

(D)
None of the above

Evaluate the derivative of
x^{3} + x^{2} + 5x
at
x = - 2

(A)
-3

(B)
-14

(C)
-2

(D)
None of the above

Find the velocity of an object described by the position function
x(t) = 3x^{2} +
at time
t = - 1

(A)
-2

(B)
5

(C)
2

(D)
-5

Find the acceleration of an object described by the position function
x(t) = 3x^{2} +
at time
t = - 1

(A)
-8

(B)
5

(C)
18

(D)
None of the above

For the following 5 questions, consider an object with position function
x(t) = (0, 0, - g)t^{2} + (2, 3, 4)t + (5, 0, 1)

What is the magnitude of the initial (ie at
t = 0
) velocity vector?

(A)
5

(B)

(C)

(D)
- g/2

What is the position of the object at time
t = - 2
?

(A)
(1, - 6, - 2g - 7)

(B)
-12

(C)
(1, - 6, - 7)

(D)
(0, 0, 0)

The object is moving

(A)
in one dimension

(B)
in two dimensions

(C)
in three dimensions

(D)
None of the above

What is the acceleration of this object at time
t = 25
?

(A)
- g

(B)
25(0, 0, -
g)

(C)
g

(D)
- (0, 0, g)

This equation might describe an object

(A)
in free fall

(B)
moving as a projectile

(C)
bouncing straight up and down

(D)
with changing acceleration

In creature-land, the measure of one's hardcoreness is directly correlated
to how high one can jump Unfortunately, creatures cannot jump straight up,
but must take a running start If creature A jumps with initial velocity
vector
(2, 2, 5)
, and creature B jumps with initial velocity vector
(5, 4, 2)
(where the
z
-direction points upwards), which creature is more
hardcore?

(A)
creature A

(B)
creature B

(C)
Both creatures are equally hardcore

(D)
Impossible to determine without knowing the gravitational acceleration in
creature-land

According to the previous question, which creature travels furthest during
its jump?

(A)
creature A

(B)
creature B

(C)
Both creatures land an equal distance away from their starting point

(D)
Impossible to determine without knowing the gravitational acceleration in
creature-land

Which function could describe the velocity of a ball being thrown
horizontally off a fire escape?

Phin and Wittgenstein are hanging out on the moon when they decide to have a
contest to see who can shoot a bullet farther Both use identical guns
Phin decides to shoot at a 60 degree angle, while Wittgenstein holds his gun
at 45 degrees when shooting Whose bullet lands the furthest away?

(A)
Phin's

(B)
Wittgenstein's

(C)
Both bullets land the same distance away

(D)
Impossible to determine without knowing the acceleration due to gravity on
the moon

The office of the Harvard Review of Philosophy is located approximately 10
ft below the earth's surface The acceleration due to gravity experienced
by members working in this office is

(A)
significantly greater than that of people on the earth's surface

(B)
significantly smaller than that of people on the earth's surface

(C)
approximately equal to that of people on the earth's surface

(D)
exactly equal to that of people on the earth's surface

A couple of students at Putney decide to go bicycle riding one day Simon
rides at a speed of 10 miles per hour, while Liz's average speed is 20 miles
per hour After bicycling for several hours, both Simon and Liz come home
and park their bicycles exactly where they started Simons's average
velocity for the entire ride is

(A)
lower than Liz's average velocity

(B)
higher than Liz's average velocity

(C)
zero

(D)
impossible to determine without knowing the actual directions in which he
biked

If, during their bike ride, Simon and Liz were always biking at a constant
speed,

(A)
their acceleration was always zero

(B)
their velocity was constant

(C)
their average velocity after one hour of biking was the same as their
average velocity after two hours of biking

(D)
None of the above

While sitting at his office desk, Stephen Greenblatt enjoys throwing
crumpled pieces of paper into a wastebasket across the room Over the
years, he has carefully kept track of all the different combinations of
initial speeds and angles at which he can throw the crumpled pieces of paper
while still making the same basket He hopes to some day have a complete
list of all the possibilities Professor Greenblatt's efforts are useless
because

(A)
although such a list can theoretically be made, he will never have enough
time to exhaust all possibilities

(B)
there is really only one way to make the basket, and Greenblatt is confused
about this because a janitor keeps moving the wastebasket at night

(C)
there are infinitely many ways to make this basket from the same position