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Name: ______________________________________________________________ Total Points: _______
(Last)
(First)
Multiple choice questions [70 points]
Answer all of the following questions. Read each question carefully. Fill the correct
bubble on your scantron sheet. Each question has exactly one correct answer. All
questions are worth the same amount of points.
1.
2.
A car starts from point A, goes 50 km in a straight line to point B,
immediately turns around, and returns to A. The time for this round
trip is 2 hours. The magnitude of the average velocity of the car for
this round trip is:
A.
r
r
∆r
r
and ∆r = 0
0 km/h v avg =
∆t
B.
C.
D.
E.
50 km/h
100 km/h
200 km/h
Cannot be calculated without knowing the acceleration
Still referring to the situation described in the previous question, what
is the average speed of the car?
A. 0 km/h
B.
50 km/h speed =
d
∆t
with d=100 km and ∆t = 2 hrs
C. 100 km/h
D. 200 km/h
E. Cannot be calculated without knowing the acceleration
3.
A ball rolls up a slope. At the end of 3 seconds its velocity is 20
cm/s; at the end of 8 seconds its velocity is 0 cm/s. What is the
magnitude of the average acceleration (in cm/s2) from the instant 3s to
the instant 8s?
A. 2.5
r
B.
r
∆v
4.0 a avg = , thus
∆t
C. 5.0
D. 6.0
E. 6.67
r
0 − 20
a avg =
= 4 cm / s 2
8−3
Name: ______________________________________________________________ Total Points: _______
(Last)
(First)
4.
As a rocket is accelerating vertically upward at 9.8 m/s2 near Earth's
surface, it releases a projectile. Immediately after release the
acceleration (in m/s2) of the projectile is:
A. 9.8 down since the projectile is free falling (it is no longer
B.
C.
D.
E.
subjected to any force by the rocket).
0
9.8 up
19.6 up
None of the above
5.
An object moves along the horizontal axis as shown on the diagram.
At which point or points is its acceleration zero?
A.
B.
C.
D.
C only
E only
B and D
A and E The acceleration is 0 when the position varies linearly
with time (x=vt+x0). On the graph, the acceleration is 0 wherever
x(t) is a straight line.
E. B, D and E
Name: ______________________________________________________________ Total Points: _______
(Last)
(First)
6.
A particle initially moving at 4.0 m/s along the x axis is uniformly
accelerated at 3.0 m/s2 along the y axis for 2.0 s. The final speed of
the particle is
A. 4.0 m/s
B. 6.3 m/s
C. 7.2 m/s
v x = 4.0 m / s 
2
2
2
2
 ⇒ v (t = 2 s ) = v x + v y = 4 + (3 × 2)
v y = 3t

D. 8.4 m/s
E. None of these is correct.
7.
-v1
∆v
The instantaneous velocity of a particle at t1 is represented by v1, and at
t2 by v2. Each heavy graph division is 10 m/s on each side. Let t1 = 1 s
and t2 = 7 s. Then the average acceleration of the particle between time
t1 and t2 is
A.
B.
C.
D.
E.
18.2
15.0
6.06
5.00
m/s2
m/s2
m/s2
m/s2
at
at
at
at
r r r
r
∆v v 2 − v1
a avg =
=
∆t
∆t
0º
180º
98º
180º
Construct ∆v as indicated above
3.03 m/s2 at 98º
Name: ______________________________________________________________ Total Points: _______
(Last)
(First)
8.
The angle between vectors A and B is 30º, and their sum is C. Which
vector diagram correctly describes the vectors A, B, and C?
A. 1
B. 2
C. 3
D. 4
E. 5
9.
r
r
A
B
has magnitude 12 m and
has magnitude 8 m.
In the diagram,
r r
The x component of A − B is about
y
r
A
45°
60°
A.
B.
C.
D.
E.
r
B
1.56 m
4.0 m
4.5 m = 12cos(45)-8cos(60)
14.4 m
20 m
x
Name: ______________________________________________________________ Total Points: _______
(Last)
(First)
10. Two objects, A and B, move with constant speed relative to a straight
line. The strobe diagram shows the positions of the objects at instant
1-3, separated by one-second time intervals. (Note that each tick mark
on the diagram represents 5 meters.)
1
2
3
A
A
A
5 meters
B
B
B
3
2
1
At instant 2 what is the direction of the instantaneous velocity of object
A in the frame of reference of object B?
A. to the left
B. to the right (see next question)
C. Undefined: the velocity is zero
11. Still referring to the problem of the previous question, at instant 2, what
is the magnitude of the instantaneous velocity of object A in the frame
of reference of object B?
A.
B.
C.
D.
E.
0 m/s
10 m/s
20 m/s
30 m/s
50 m/s
Since the velocities are constant, instantaneous and average
velocities are equal. Compute the average velocity between for
instance instant t1 and instant t2
r
r
rA / B (t 2 ) − rA / B (t1 ) (−2 × 5) xˆ − (−12 × 5) xˆ
r
=
= 50m / s xˆ
vA/ B =
1
t 2 − t1
where xˆ is a unit vector directed to the right.
Name: ______________________________________________________________ Total Points: _______
(Last)
(First)
12. A girl on a merry-go-round moves horizontally in a circle at constant
speed. She travels one fourth of a revolution , a distance of 25m along
the circumference of the circle, in 5.0s. The magnitude of her
acceleration is
A. 0.31 m/s2
B. 1.3 m/s2
C.
2
1.6 m/s a =
D. 3.9 m/s2
E. 6.3 m/s2
v 2 (25 / 5) 2
=
=π /2
25
R
π /2
Name: ______________________________________________________________ Total Points: _______
(Last)
(First)
10 m
PROBLEM [40 points]
A boy hurls a stone with a sling shot at a
flying line of Canada geese. The stone is
thrown at 30m/s vertically upward exactly
when the first of the line of geese is overhead
(t=0). The geese fly 4m/s, 10 m apart at an
altitude of 25m (counted from the position of
the stone at t=0). Take g=10 m/s2
y
4 m/s
25 m
30 m/s
x
1). [10 pts] If the boy misses the geese, when does the stone reach its
maximum height?
The velocity is 0 at t such that
v = −10t + 30 ⇒ t = 3s
2). [15 pts] When does the stone cross the path of the geese (make sure that you
count all possible crossings)?
Solve y=25m for t
1
− × 10t 2 + 30t = 25 ⇒ t = 1s and t = 5s
2
3). [15 pts] Does the stone hit a goose; if so which one (first goose is #1)?
The position of goose n is given by
x n = 4t − 10(n − 1)
To be hit the goose crosses the path of the stone (xn=0) at t=1s or at t=5s
14
, no goose is hit since n must be an integer
10
30
at t=5s, xn=0 ⇒ n =
= 3 , goose 3 is hit.
10
at t=1s, xn=0 ⇒ n =
1/--pages
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