In the following problems, vectors are designated by letters with an arrow above them and the
unit vectors in the positive x, y, and z directions are denoted by iˆ , jˆ and kˆ , respectively.
1. A car is driven due east for 30 min at a speed of 50 km/h, then due west for 45 min at a speed
of 100 km/h. For the whole trip, the magnitude of the average velocity is _____ km/h and the
direction of the average velocity is _____.
A. 40, west
B. 80, east
C. 25, west
D. 50, east
E. 25, west
2. The position x of a particle moving in one dimension is given by
x = 4.0m + (16m s ) − (1.0m s2 )t 2 + (1.0m s3 )t 3 , where t is the time in seconds. The
acceleration of the particle at time t = 2.0 s is _____ m/s2.
A. - 18
B. - 8
C. 0
D. 6
E. 24
3. A baseball is thrown vertically up at a speed of 19.6 m/s. The time that the baseball takes to
reach its maximum height is ______ s. (Neglect the influence of the air on the motion.)
A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5
4. A car accelerates from rest in a straight line at a rate of 2.0 m/s2. The speed of the car after
the car has traveled 100 m is _____ m/s.
A. 5
B. 10
C. 15
D. 20
E. 25
r r
r
5. Three vectors a , b and c are given by
r
a = (−3.0m)iˆ + ( −5.6m ) jˆ + ( −3.0m)kˆ
r
b = (1.5m)iˆ + ( −1.1m) jˆ + (−4.0)kˆ
r
c
= (0.5mr)iˆ + ( 1.5m
) jˆ + (1.0m )kˆ
r
r
r
r
r
The vector d is given by d = a − b + 3 c . The magnitude of d is _____ m.
A. 1.0
B. 2.0
C. 3.0
D. 4.0
E. 5.0
D. 4.4
E. 1.7
6. A 4.0 kg block starts from rest and slides 20 m
down an incline plane with constant acceleration
in 3 seconds. The acceleration is ______ m/s2 .
A. 60
B. 6.7
C. 5.0
7. A ball is projected vertically downward at 2.00 m/s from a bridge and is found to hit the
water 1.50 s later. Assuming the only force is gravity, the height of the bridge is ____ m.
A. 3.0
B. 8.0
C. 11.0
D. 14.0
E. 17.0
8. A particle that starts from rest at the origin at t = 0,
has a velocity vs. time curve shown at the right. At t
= 0 s, the acceleration is ______ m/s2 and the
displacement from the origin is _____ m.
A. 0.67, 8
B. 0.67, 5
C. 0, 8
D. 0, 5
E. none of the above
9. A 4.0 kg ball is swung in a horizontal circle of 2.0 radius so that the tension in the rope is 8.0
N. If you ignore gravity, the speed of the ball is _____ m/s.
A. 2.0
B. 4.0
C. 8.0
D. 16.0
E. none of the above
D. 9.8, 29
E. none of the above
10. A 3 kg block under gravity pulls an 8 kg block
along a frictionless surface. The acceleration
of the 3 kg block is ______ m/s2 and the
tension in the rope is _____ N.
A. 2.7, 21
B. 5.9, 18
C. 7.1, 22
11. A force of 16 N causes a 3.0 kg and a 5.0 kg block
to accelerate to the right across a frictionless plane.
The net force on the 3.0 kg block is _____ N.
A. 6
B. 8
C. 10
D. 16
E. none of the above
12. An 8 kg block rests on an inclined plane at angle θ
to the horizontal. As θ gradually increases from
zero toward 90°, the block suddenly flips at θ =
37°. The coefficient of static friction is ______.
A. 6.0
B. 0.80
C. 0.75
D. 0.60
E. none of the above
13. A cannon on a hill projects a shell with a velocity of
20 m/s at 30° above the horizontal to a plain 40 m
below the level of the gun. Ignoring all forces but
gravity, the time of flight of the shell is _____ N.
A. 2.9
B. 4.0
C. 5.3
D. 6.7
E. 7.1
14. A horizontal force of 3.0 N holds a ball of
mass m at rest at an angle of 20° to the vertical.
The tension in the rope is _____ N.
A. Cannot tell with knowing
the mass of the ball.
B. 3.0
C. 3.3
D. 8.2
E. 8.8
15. A test car was able to travel around a flat circular track of radisu r = 45.7 m at a speed of 18.9
m/s without slipping. At a slightly faster speed the wheels slip. The coefficient of static
friction is ________.
A. 0.80
B. 0.61
C. 0.45
D. 0.23
E. Cannot tell with knowing
the mass of the car.
16. The Earth is approximately spherical with a mean radius of 6370 km. The volume of the
Earth is _____ cm3.
A. 1.1× 1021
B. 9.3 ×10 24
C. 1.1× 1027
D. 5.4 × 1029
E. 3.7 × 1031
17. Which one of following five statements is true?
A. If a particle undergoes one-dimensional motion along the x-axis, the acceleration of the
particle at a given time is the slope of the tangent line at that time on a plot of the particle
position x versus time.
B. For a particle undergoing vertical free-fall motion, the shape of a plot of the particle's position
y versus time is a hyperbola if the influence of the air on the motion can be neglected.
C. The displacement of a particle between two times is a scalar quantity.
D. The acceleration of a particle can be in the opposite direction to the velocity of the particle.
E. The average speed of a particle between two times is always the same as the magnitude of the
average velocity between those two times.
18. Which one of following five statements is true?
A. In a right-handed Cartesian coordinate system, the vector units iˆ , jˆ and kˆ satisfy the vector
product relation iˆ × jˆ = kˆ .
B. A unit vector in a vector component
vector has units of meters.
r r r of a rposition
r
r
C. For any two vectors a and b , a + b = − b + a .
(
)
D. The scalar components of a vector are always either positive or zero.
E. If the angle between two vectors is varied while keeping the magnitude of each of the two
vectors constant, the magnitude of the scalar (dot) product of the two vectors is maximum
when the two vectors are perpendicular to each other.
r
r
19. The vector a is given by a = (−3.0m)iˆ + ( 4.0m) jˆ . The magnitude of the vector is ____ m and
the angle (including its correct sign) between the vector and the positive x-axis is ____°.
A. 5.0, -53
B. 1.0, -37
C. 0.5, 159
D. 5.0, 143
E. 5.0, 127
r
r
20. Let a and b be vectors
with magnitude a and b, respectively, where the interior angle
r
r
between a and
b is φ rwhen the two vectors are placed tail-to-tail. The value of the dot
r r
r
product a + b • a + b is
(
) (
A. (a 2 + b2 ) sin2
B. a2 + b2 + 2ab cos
C. (a 2 + b2 ) cos
)
D. (a 2 + b2 ) sin(2
)
E. a + b − 2abcos
21. A ball is thrown vertically upward with initial velocity of +15 m/s. At the top of the path, the
velocity is ______ m/s and the acceleration is ______ m/s2.
2
2
A. 15, +9.81
B. 0, +9.81
C. 0, -9.81
D. 0, 0
E. 15, 0
22. A horizontal force of 20 N pulls a 10 kg sled across a smooth horizontal floor at a constant
velocity of 1.5 m/s. The coefficient of kinetic friction is
A. 0.8
B. 0.4
C. 0.2
D. 0.08
E. can't tell from this information
23. A woman pullsa crate that does not move with a force of 10 N. Rank the situations below
according to the magnitude of the friction force exerted on the crate by the surface from
smallest to largest.
A. 1, 2, 3
B. 2, 1, 3
C. 2, 3, 1
D. 1, 3, 2
E. 3, 2, 1
D. +2.0
E. –2.0
24. For the diagram shown, the velocity at
t = 1.0 s is _____ m/s.
A. zero
B. +1.0
C. –1.0
25. A block of mass m starts from rest and slides
down a frictionless plane set at angle θ above
the horizontal. The acceleration of the block is
_____ m/s2.
A. v 2 r
B.
gr
C. g sin
D. gcos
E. gsin
26. Which of the following quantities is (are) vectors?
1) mass
2) displacement
3) temperature
4) force
5) acceleration
A. 2 only
B. 1 and 3 only
C. 2 and 4 only
D. 2, 4, and 5 only
E. 1, 2, 4, and 5 only
27. Ignoring air resistance, a ball thrown horizontally from the roof of a building will follow a
_______ path.
A. hyperbolic
B. circular
C. straight line D. parabolic
E. none of these
28. A bullet show horizontally from a gun will strike the ground _______ a bullet dropped
vertically from the same point at the same time. Ignore air resistance and the curvature of the
earth.
A. later than
B. sooner than
C. at the same time as
29. A girl wishes to row due north directly across a river that flows from west to east. She rows
at 2 m/s relative to the water and the river flows at 1 m/s relative to the ground. She should
point the boat _______.
A. due north
B. 30° east of north
C. 30° west of north
D. 45° west of north
E. 45° east of north
30. Ignoring air resistance, the range of a cannon is maximum when fired at an angle of _______
degrees above the horizontal
A. 20
B. 30
C. 45
D. 60
E. none of these