Vector quantities are represented in terms of their magnitude and direction.

Exam Review I
Name___________________________________
TRUE/FALSE.  Write 'T' if the statement is true and 'F' if the statement is false.
1) Vector quantities are represented in terms of their magnitude and direction. 1)
2) If A+ B=0, then the vectors A and B have equal magnitudes and are directed in the same
direction.
2)
3) Free fall is the motion of an object subject only to the influence of gravity. 3)
4) If A+ B= C and A+B=C, then the vectors A and B are oriented perpendicular relative to one
other.
4)
5) The horizontal component of the velocity of a projectile remains constant during the entire
trajectory of the projectile.
5)
6) A ball is thrown at an angle of Ό above the horizontal. If there is no acceleration due to gravity the
ball will follow a straight-line path.
6)
7) An object thrown downward does not experience free fall. 7)
MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.
8) If a vector A has components Ax > 0, and Ay > 0, then the angle that this vector makes with the
positive x-axis must be in the range
8)
A) 0° to 90°.XXX
B) 90° to 180°.
C ) 180° to 270°.
D) 270° to 360°.
E) cannot be determined without additional information
9) You drive 6.00 km at 50.0 km/h and then another 6.00 km at 90.0 km/h. Your average speed over
the 12.0 km drive will be
9)
A) exactly 38.0 km/h.
B) greater than 70.0 km/h.
C ) less than 70.0 km/h.XXX
D) equal to 70.0 km/h.
E) cannot be determined from the information given, must also know directions traveled
10) When is the average velocity of an object equal to the instantaneous velocity? 10)
A) only when the velocity is constantXXX
B) only when the velocity is increasing at a constant rate
C ) only when the velocity is decreasing at a constant rate
D) n e v e r
E) a l w a y s
111) Suppose that an object is moving with a constant velocity.  Make a statement concerning its
acceleration.
11)
A) The acceleration must be constantly increasing.
B) The acceleration must be equal to zero.XXX
C ) The acceleration must be constantly decreasing.
D) The acceleration must be a constant non-zero value.
E) A statement cannot be made without additional information.
12) The slope of a tangent line at a given time value on a velocity versus time graph gives 12)
A) displacement.
B) instantaneous velocity.
C ) instantaneous acceleration.XXX
D) average acceleration.
E) average velocity.
13) An object is moving with constant non-zero velocity in the +x-axis.  The position versus time
graph of this object is
13)
A) a vertical straight line.
B) a straight line making an angle with the time axis.XXX
C ) a   p a r a b o l i c   c u r v e .
D) a hyperbolic curve.
E) a horizontal straight line.
14) The area under a curve in a velocity versus time graph gives 14)
A) distance traveled.
B) acceleration.
C ) velocity.
D) displacement.XXX
E) speed.
15) Two athletes jump straight up. John has twice the initial speed of Harry. Compared to Harry, John
jumps
15)
A) four times as long.XXX
B) 1.41 times as long.
C ) three times as long.
D) 0.50 times as long.
E) twice as long.
16) You drop a stone from a bridge to the river below. After this stone has traveled a distance d, you
drop a second stone. The distance between the two stones will always
16)
A) increases at first, but then stays constant.
B) increases.XXX
C ) decreases at first, but then stays constant.
D) decreases.
E) stays constant.
2FIGURE 2-6
17) Refer to Figure 2-6. If you start from the Bakery, travel to the Cafe, and then to the Art Gallery,
what is the magnitude of your displacement?
17)
A) 10.5 km
B) 6.5 km
C ) 1.5 km
D) 2.5 kmXXX
E) 9.0 km
18) A car is making a 12-mile trip. It travels the first 6.0 miles at 30 miles per hour and the last 6.0
miles at 60 miles per hour. What is the car's average speed for the entire trip?
18)
A) 45 mph
B) 20 mph
C ) 5 0   m p h
D) 35 mph
E) 40 mphXXX
FIGURE 2-7
19) Figure 2-7 represents the position of a particle as it travels along the x-axis. What is the average
speed of the particle between t = 1 s and t = 4 s?
19)
A) 0.50 m/s
B) 1.3 m/sXXX
C ) 0.25 m/s
D) 1.0 m/s
E) 0.67 m/s
3FIGURE 2-9
20) Figure 2-9 represents the velocity of a particle as it travels along the x-axis. What is the average
acceleration of the particle between t = 1 second and t = 4 seconds?
20)
A) 2.0 m/s2
B) 3.0 m/s2
C ) 1.7 m/s2X X X
D) 0.33 m/s2
E) 2.5 m/s2
FIGURE 2-10
21) Figure 2-10 shows the velocity-v e r s u s-time graph for a basketball player traveling up and down
the court in a straight-line path. Find the net displacement of the player for the 10 s shown on the
g r a p h .
21)
A) 18 mXXX B) 14 m C ) 12 m D) 20 m E) 16 m
22) An airplane starts from rest and accelerates at 10.8 m/s2. What is its speed at the end of a 400
m-long runway?
22)
A) 37.0 m/s
B) 93.0 m/sXXX
C ) 4320 m/s
D) 186 m/s
E) 65.7 m/s
423) A car is traveling at 30.0 m/s when the driver suddenly applies the brakes, giving the car a
constant deceleration. The car comes to a stop in a distance of 120.0 m. What was the deceleration
of the car?
23)
A) 4.25 m/s2
B) 4.75 m/s2
C ) 4.00 m/s2
D) 4.50 m/s2
E) 3.75 m/s2X X X
24) Car A is traveling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind car B when the driver of
car A accelerates his car with an acceleration of 2.40 m/s2. How long does it take car A to overtake
car B?
24)
A) 12.6 s
B) 5.50 s
C ) 19.0  s X X X
D) 316 s
E) Car A never overtakes car B.
25) An object is thrown upwards with a speed of 14 m/s. How high above the projection point does it
reach?
25)
A) 20 m B) 25 m C ) 10 mXXX D) 5.0 m E) 15 m
26) An object is thrown upwards with a speed of 14 .0 m/s. How long does it take it to reach its
maximum height?
26)
A) 1.22 s B) 3.14 s C ) 1.43 sXXX D) 5.31 s E) 4.15 s
27) An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/
s2. To determine the depth of the crater, she drops a rock and measures the time it takes for it to
hit the bottom. If the depth of the crater is 120 m, how long does it take for the rock to fall?
27)
A) 3.04 s B) 32.1 s C ) 12.2 sXXX D) 37.5 s E) 29.3 s
28) The national debt is measured in trillions of dollars. Which of the following is a representation of a
trillion?
28)
A) 1 × 103
B) 1 × 109
C ) 1 × 1015
D) 1 × 106
E) 1 × 1012 XXX
29) If you are measuring the length of a room, the most appropriate SI unit is the 29)
A) centimeter.
B) meter.XXX
C ) micrometer.
D) millimeter.
E) kilometer.
530) When multiplying several quantities, the number of significant digits in the result must always be 30)
A) equal to the number of significant digits in the least accurate of the quantities.XXX
B) larger than the number of significant digits in the most accurate of the quantities.
C ) smaller than the number of significant digits in the least accurate of the quantities.
D) equal to the number of significant digits in the most accurate of the quantities.
E) equal to the average number of significant digits in the most and least accurate of the
q u a n t i t i e s .
31) What is the conversion factor between km/h and m/s? 31)
A) 2.78 × 10-1  m / s X X X
B) 3.60 m/s
C ) 7.72 × 10-5 m/s
D) 16.7 m/s
E) 1.30 × 104 m/s
32) A vector quantity is defined as 32)
A) a quantity that is specified by a numerical value only.
B) a quantity that is specified by using both a numerical value and a direction.XXX
33) The density of a solid object is defined as the ratio of the mass of the object to its volume. The
dimension of density is
33)
A) [M][L].
B) [M][ L ]-3.XXX
C ) [M][L][T].
D) [M]/[L].
E) [ L ]3/[M].
34) How many significant figures are in 10,002? 34)
A) 5XXX
B) 3
C ) 2
D) 4
E) a m b i g u o u s
35) A train travels at a constant speed of 60.4 miles per hour for 101.5 minutes. What distance does the
train cover?
35)
A) 102 milesXXX
B) 100 miles
C ) 102.2 miles
D) 102.181 miles
E) 102.18 miles
36) The Hoover Dam is 726 feet high. What is its height in kilometers? 36)
A) 0.221 kilometersXXX
B) 0.138 kilometers
C ) 0.525 kilometers
D) 0.726 kilometers
E) 0.275 kilometers
6FIGURE 3-3
37) Refer to Figure 3-3. Three forces F1 = F2= F3= 70 N are acting on an object O as shown in the
figure. Which one of the following statements is true regarding the resultant force acting over the
object O?
37)
A) The resultant force is zero.XXX
B) The resultant force is 35 N.
C ) The resultant force is 140 N.
D) The resultant force is 210 N.
E) The resultant force is 70 N.
38) Vector A = 6.0 m and points 30° north of east. Vector B = 4.0 m and points 30° west of north. The
resultant vector A + B is given by
38)
A) 9.8 m at an angle 26° north of east.
B) 9.8 m at an angle 64° east of north.
C ) 7.2 m at an angle 26° east of north.XXX
D) 3.3 m at an angle 26° north of east.
E) 3.3 m at an angle 64° east of north.
39) What is the smallest number of vectors that can be added to give a zero resultant? 39)
A) 2XXX
B) 3
C ) 4
D) 5
E) You cannot add vectors and obtain a zero resultant.
40) The eastward component of vector A is equal to the westward component of vector B and their
northward components are equal. Which one of the following statements is correct for these two
v e c t o r s ?
40)
A) Vector A is perpendicular to vector B .
B) Magnitude of vector A is equal to the magnitude of vector B .XXX
C ) Magnitude of vector A is twice the magnitude of vector B.
D) Vector A is parallel to vector B .
E) Vector A is anti-parallel to vector B .
741) Vector A = 6.0 m and points 30° south of east. Vector B = 4.0 m and points 30° east of south. The
resultant vector A + B is given by
41)
A) 4.7 m at an angle 42° south of east.
B) 1.1 m at an angle 42° south of east.
C ) 13.7 m at an angle 42° south of east.
D) 0.7 m at an angle 42° south of east.
E) 9.7 m at an angle 42° south of east.XXX
42) Vector A = 8.0 m and points east, Vector B = 6.0 m and points north, and vector C = 5.0 m and
points west. The resultant vector A + B + C is given by
42)
A) 3.8 m at an angle 67° north of east
B) 2.0 m at an angle 63° north of east.
C ) 6.7 m at an angle 63° north of east.XXX
D) 6.7 m at an angle 63° east of north.
E) 2.0 m at an angle 63° east of north.
FIGURE 3-5
43) Refer to Figure 3-5. The components of the sum of these vectors are given by
choice x-component y-component
1
2
3
4
5
0   c m
-3.5 cm
+3.5 cm
0   c m
0   c m
+6.0 cm
-2.0 cm
-2.0 cm
-4.0 cm
-2.0 cm
43)
A) Choice 1
B) Choice 2
C ) Choice 3
D) Choice 4XXX
E) Choice 5
8FIGURE 3-7
44) The magnitudes of the four vectors shown in Figure 3-7 are given as follows: A = 10.0 m, B = 8.0
m ,
C = 6.0 m, and D = 2.0 m. The components of the vector sum of these four vectors are
Choice x-component y-component
1
2
3
4
5
  1.5 m
13.5 m
  3.5 m
-2.9 m
18.1 m
   6.0 m
  20.0 m
  14.0 m
-14.0 m
-5.0
44)
A) Choice 1
B) Choice 2
C ) Choice 3XXX
D) Choice 4
E) Choice 5
45)
^ ^
^ ^
A car is moving with a velocity (3.0 m/s)x + (1.0 m/s)y and 3.0 seconds later its velocity is (6.0 m/s)
x - (3.0 m/s)y. What is the direction of the average acceleration of the car?
45)
A) -53° from the x-axisXXX
B) 67° from the x-axis
C ) -67° from the x-axis
D) 53° from the x-axis
E) 60° from the x-axis
46)
^ ^ ^ ^
Vector A = 2.00 x + -1.00 y and vector B = 3.00 x + 4.00 y.  What is vector C = A - B? 46)
A)
^ ^
-1.00 x + -3.00 y
B)
^
^
^
1.00 x + 3.00 y
C )
^ ^
1.00 x + 5.00 y
D)
^ ^
-1.00 x + -5.00 yX X X
E)
^ ^
-1.00 x + 3.00 y
9FIGURE 3-9
47) Refer to Figure 3-9. The components of the sum of these vectors are given by
Choice x-component y-component
1
2
3
4
5
4.9 cm
2.8 cm
0   c m
-4.2 cm
0   c m
2.8 cm
4.9 cm
4.2 cm
0   c m
4.2 cm
47)
A) Choice 1
B) Choice 2
C ) Choice 3XXX
D) Choice 4
E) Choice 5
48) If the acceleration vector of an object is directed parallel to the velocity vector, 48)
A) the object is not moving.
B) the object is speeding up.XXX
C ) the object is turning.
D) the object is slowing down.
E) this situation would not be physically possible.
49) A rock is thrown at some angle above the horizontal with a certain velocity. It reaches its highest
point and starts falling down. What is the velocity of the rock at the highest point of its trajectory?
49)
A) 0
B) 9.8 m/s
C ) It is equal to its initial velocity.
D) It is equal to its initial vertical velocity.
E) It is equal to its initial horizontal velocity.XXX
50) A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. The
magnitude of the acceleration of the ball while it is in flight is
50)
A) 0 m/s2.
B) 25 m/s2.
C ) 9.8 m/s2.XXX
D) 20 m/s2.
E) 8.4 m/s2.
1051) If the initial speed of a projectile is doubled. 51)
A) Its range will decrease by a factor of four.
B) Its range will quadruple.XXX
C ) Its range will double.
D) Its range will be decreased by a factor of two.
E) Its range will be increased by 1.41.
52) A bullet is fired with a certain velocity at an angle Ό above the horizontal at a location where g =
10.0 m/s2. The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively.
What is the initial velocity of the bullet?
52)
A) 100 m/sXXX
B) 86.6 m/s
C ) 50.0 m/s
D) 36.6 m/s
E) 136 m/s
53) A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The
ball leaves her hand 1.00 m above the ground. At what angle below the horizontal does the ball
approach the ground?
53)
A) 35.1° B) 65.2° C ) 38.6° D) 48.0° XXX E) 40.0°
54) An athlete competing in long jump leaves the ground with a speed of 9.14 m/s at an angle of 35.0°
above the horizontal. How long does the athlete stay in the air?
54)
A) 1.07 sXXX B) 0.535 s C ) 2.53 s D) 0.876 s E) 0.501 s
55) A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The
ball leaves her hand 1.00 m above the ground. How far from where the child is standing does the
ball hit the ground?
55)
A) 1.22 m
B) 1.58 m
C ) 6.79 m
D) 7.46 mXXX
E) 5.14 m
56) A ball is thrown with an initial speed of 60 m/s at an angle of 30° above the horizontal. What is the
ball's horizontal displacement at the end of 4 seconds? Use g = 10 m/s2.
56)
A) 120 m B) 240 m C ) 140 m D) 210 mXXX E) 60 m
57) A person throws a ball horizontally from the top of a building that is 40.0 m high. The initial
velocity of the ball is 100 m/s. What is the horizontal distance that the ball travels before hitting the
g r o u n d ?
57)
A) 100 m B) 286 mXXX C ) 572 m D) 325 m E) 367 m
58) A ball rolls off the edge of a table with an initial velocity of 20 m/s. The height of the table above
the ground is 2.0 m. How long does it take the ball to reach the ground?
58)
A) 0.98 s B) 0.32 s C ) 0.64 sXXX D) 2.0 s E) 0.49 s
1159) A ball is thrown horizontally with an initial velocity of 40 m/s from a height of 10 m. How long
will it take for the ball to touch the ground? Use g = 10 m/s2.
59)
A) 2.4 seconds
B) 1.0 second
C ) 0.70 second
D) 1.4 secondsXXX
E) 2.0 seconds
60) For which value of Ό is the range of a projectile fired from ground level a maximum? 60)
A) 55° above the horizontal
B) 30° above the horizontal
C ) 60° above the horizontal
D) 90° above the horizontal
E) 45° above the horizontalXXX
61) A boy kicks a football from ground level with a certain initial velocity at an angle 30.0° above the
horizontal. In 2.00 seconds the ball completes its trajectory and hits the ground. What is the initial
velocity of the ball?
61)
A) 4.90 m/s
B) 19.6 m/sXXX
C ) 39.2 m/s
D) 9.80 m/s
E) 78.4 m/s
62) A ball is thrown at an angle 40.0° above the horizontal with an initial velocity of 28.0 m/s. What is
the range of the ball?
62)
A) 37.8 m
B) 59.8 m
C ) 78.8 mXXX
D) 19.6 m
E) None of the other choices is correct.
12

Physics Acceleration Deceleration Problems

1. A car is traveling at 26.0 m/s when the driver suddenly applies the brakes, giving the car a constant deceleration. The car comes to a stop in a distance of 120.0 m. How fast was the car moving when it was 60.0 m past the point where the brakes were applied?

A. 22.52 m/s B. 18.4 m/s C. 15.0 m/s D. 12.1 m/s

2. A car is traveling at 24.0 m/s when the driver suddenly applies the brakes, giving the car a constant deceleration. The car comes to a stop in a distance of 120.0 m. How fast was the car moving when it was 30.0 m past the point where the brakes were applied?

A. 7.50 m/s B. 15.0 m/s C. 23.5 m/s D. 20.8 m/s

3. A car is traveling with a constant speed when the driver suddenly applies the brakes, giving the car a deceleration of 3.50 m/s2 .The car comes to a stop in a distance of 34.0 m. What was the car's speed when it had traveled 17.0 m from the point where the brakes were applied?

A. 10.9 m/s B. 14.5 m/s C. 10.7 m/s D. 21.0 m/s

4. A car is traveling with a constant speed when the driver suddenly applies the brakes, giving the car a deceleration of 3.50 m/s2. If the car comes to a stop in a distance of 30.0 m, what was the car's original speed?

A. 10.2 m/s B. 14.5 m/s C. 2.5105 m/s D. 2.5210 m/s

5. A car traveling with velocity v is decelerated by a constant acceleration of magnitude a. It takes a time t to come to rest. If its initial velocity were doubled, the time required to stop would

A. double as well
B. Decrease by a factor of 2
C. Stay the Same
D. Quadruple.


We nned to calculate the acceleration using v^2 = v0^2 + 2*a*x..
since v = 0 then a = -v0^2/2x = -26^2/(2*120) = -2.817m/s^2

So when the car has gone 60m we find
v = sqrt(v0^2 + 2*a*x) = sqrt(26^2 + 2*(-2.817)*60) = 18.4m/s

2. Just like the one above with different numbers

3. First we find v0 using the v^2 = v0^2 + 2*a*x eqn where v = 0
we get v0 = sqrt(2*a*x) = sqrt(2*3.50*34) = 15.4m/s
So now when x = 17 we get v = sqrt(15.4^2 + 2*(-3.50)*17) = 10.9m/s

4.JUst like #3 above Solve using different numbers

5. Using v = v0 - a*t when it stops v = 0 ...so v0 = at..or t = v0/a
So if v0 is doubled then time is doubled