# vectors &amp; motion

True
Consider a deer that runs from point A to point B. The distance the deer runs can be greater than the magnitude of its displacement, but the magnitude of the displacement can never be greater than the distance it runs.
(T orF)
B) 40 KM southwest
E) 186,000 miles
2) Which of the following quantities has units of a displacement? (There could be more than one
correct choice.)

A) 32 ft/s2 vertically downward

B) 40 km southwest

C) 9.8 m/s2

D) -120 m/s

E) 186,000 mi

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C) The displacement is either less than or equal to the distance traveled.
Suppose that an object travels from one point in space to another. Make a comparison between the magnitude of the displacement and the distance traveled by this object.
A) The displacement is either greater than or equal to the distance traveled.

B) The displacement is always equal to the distance traveled.

C) The displacement is either less than or equal to the distance traveled.

D) The displacement can be either greater than, smaller than, or equal to the distance traveled.

C) when the velocity is constant
When is the average velocity of an object equal to the instantaneous velocity?

A) only when the velocity is increasing at a constant rate

B) only when the velocity is decreasing at a constant rate

C) when the velocity is constant

D) always

E) never

C) less than 70 km/h.
7) You drive 6.0 km at 50 km/h and then another 6.0 km at 90 km/h. Your average speed over the 12 km drive will be

A) greater than 70 km/h.

B) equal to 70 km/h.

C) less than 70 km/h.

D) exactly 38 km/h.

E) It cannot be determined from the information given because we must also know directions traveled.

True
Consider a car that travels between points A and B. The car’s average speed can be greater than the magnitude of its average velocity, but the magnitude of its average velocity can never be greater than its average speed.
(T or F)
False
If the velocity of an object is zero at some point, then its acceleration must also be zero at that point.
(t or f)
E) An object has constant non-zero velocity and changing acceleration.
Which of the following situations is impossible?

A) An object has velocity directed east and acceleration directed west.

B) An object has velocity directed east and acceleration directed east.

C) An object has zero velocity but non-zero acceleration.

D) An object has constant non-zero acceleration and changing velocity.

E) An object has constant non-zero velocity and changing acceleration.

False
If the acceleration of an object is zero, then that object cannot be moving.
(t or f)
False
If the velocity of an object is zero, then that object cannot be accelerating.
(t or f)
A) The acceleration is toward the east.
Suppose that a car traveling to the west begins to slow down as it approaches a traffic light. Which of the following statements about its acceleration is correct?

A) The acceleration is toward the east.

B) Since the car is slowing down, its acceleration must be negative.

C) The acceleration is zero.

D) The acceleration is toward the west.

C) average acceleration
13) An auto manufacturer advertises that their car can go “from zero to sixty in eight seconds.” This is a description of what characteristic of the car’s motion?

A) average speed

B) instantaneous speed

C) average acceleration

D) instantaneous acceleration

E) displacement

D) is increasing its velocity by 2.0 m/s every second.
An object moving in the +x direction experiences an acceleration of +2.0 m/s2. This means the object

A) travels 2.0 m in every second.

B) is traveling at 2.0 m/s.

C) is decreasing its velocity by 2.0 m/s every second.

D) is increasing its velocity by 2.0 m/s every second.

B) Its acceleration is in the -x direction.
Suppose that a car traveling to the east (+x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct?

A) Its acceleration is in the +x direction.

B) Its acceleration is in the -x direction.

C) Its acceleration is zero.

D) Its acceleration is decreasing in magnitude as the car slows down.

A) Its acceleration is positive.
Suppose that a car traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct?

A) Its acceleration is positive.

B) Its acceleration is negative.

C) Its acceleration is zero.

D) Its acceleration is decreasing in magnitude as the car slows down.

D) The acceleration is equal to zero.
Suppose that an object is moving with a constant velocity. Which statement concerning its acceleration must be correct?

A) The acceleration is constantly increasing.

B) The acceleration is constantly decreasing.

C) The acceleration is a constant non-zero value.

D) The acceleration is equal to zero.

A) The acceleration could be positive.

B) The acceleration could be negative.

C) The acceleration could be zero.

18) If the velocity of an object is zero at one instant, what is true about the acceleration of that object? (There could be more than one correct choice.)

A) The acceleration could be positive.

B) The acceleration could be negative.

C) The acceleration could be zero.

D) The acceleration must be zero.

B) The acceleration is constant.
Under what condition is average velocity equal to the average of the object’s initial and final velocity?

A) This can only occur if there is no acceleration.

B) The acceleration is constant.

C) This can occur only when the velocity is zero.

D) The acceleration must be constantly increasing.

E) The acceleration must be constantly decreasing.

A) Before marker 1
A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at half this speed, that is at 70 km/h?

A) Before marker 1

B) At marker 1

C) Between marker 1 and marker 2

B) is downward
21) When a ball is thrown straight up with no air resistance, the acceleration at its highest point

A) is upward

B) is downward

C) is zero

D) reverses from upward to downward

E) reverses from downward to upward

D) The acceleration is downward at all points in the motion.
22) A rock from a volcanic eruption is launched straight up into the air with no appreciable air resistance. Which one of the following statements about this rock while it is in the air is correct?

A) On the way up, its acceleration is downward and its velocity is upward, and at the highest point both its velocity and acceleration are zero.

B) On the way down, both its velocity and acceleration are downward, and at the highest point both its velocity and acceleration are zero.

C) Throughout the motion, the acceleration is downward, and the velocity is always in the same direction as the acceleration.

D) The acceleration is downward at all points in the motion.

E) The acceleration is downward at all points in the motion except that is zero at the highest point.

C) exactly g
23) Suppose a ball is thrown straight up and experiences no appreciable air resistance. What is its acceleration just before it reaches its highest point?

A) zero

B) slightly less than g

C) exactly g

D) slightly greater than g

B) Its velocity points upward and its acceleration points downward
A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Which of the following statements about the direction of the velocity and acceleration of the ball as it is going up is correct?

A) Both its velocity and its acceleration point upward.

B) Its velocity points upward and its acceleration points downward.

C) Its velocity points downward and its acceleration points upward.

D) Both its velocity and its acceleration points downward.

B) Its acceleration is constant.
A ball is thrown downward in the absence of air resistance. After it has been released, which statement(s) concerning its acceleration is correct? (There could be more than one correct choice.)

A) Its acceleration is constantly increasing.

B) Its acceleration is constant.

C) Its acceleration is constantly decreasing.

D) Its acceleration is zero.

E) Its acceleration is greater than g.

C) h
A 10-kg rock and a 20-kg rock are thrown upward with the same initial speed v0 and experience no significant air resistance. If the 10-kg rock reaches a maximum height h, what maximum height will the 20-kg ball reach?

A) h/4

B) h/2

C) h

D) 2h

E) 4h

C) T
27) A 10-kg rock and 20-kg rock are dropped from the same height and experience no significant air resistance. If it takes the 20-kg rock a time T to reach the ground, what time will it take the 10-kg rock to reach the ground?

A) 4T

B) 2T

C) T

D) T/2

E) T/4

C) a
A 10-kg rock and a 20-kg rock are dropped at the same time and experience no significant air resistance. If the 10-kg rock falls with acceleration a, what is the acceleration of the 20-kg rock?

A) 4a

B) 2a

C) a

D) a/2

E) a/4

A) increases.
29) Two objects are dropped from a bridge, an interval of 1.0 s apart. Air resistance is negligible. During the time that both objects continue to fall, their separation

A) increases.

B) decreases.

C) stays constant.

D) increases at first, but then stays constant.

E) decreases at first, but then stays constant.

C) the two balls will have the same speed.
From the edge of a roof top you toss a green ball upwards with initial speed v0 and a blue ball downwards with the same initial speed. Air resistance is negligible. When they reach the

ground below

A) the green ball will be moving faster than the blue ball.

B) the blue ball will be moving faster than the green ball.

C) the two balls will have the same speed.

B) remains constant.
Ball A is dropped from the top of a building. One second later, ball B is dropped from the same building. Neglect air resistance. As time progresses, the difference in their speeds

A) increases.

B) remains constant.

C) decreases.

D) cannot be determined from the information given.

C) They are traveling at the same speed.
Two objects are thrown from the top of a tall building. One is thrown up, and the other is thrown down, both with the same initial speed. What are their speeds when they hit the street? Neglect air resistance.

A) The one thrown up is traveling faster.

B) The one thrown down is traveling faster.

C) They are traveling at the same speed.

D) It is impossible to tell because the height of the building is not given.

C) The two bricks have exactly the same acceleration.
Brick A is dropped from the top of a building. Brick B is thrown straight down from the same building, and neither one experiences appreciable air resistance. Which statement about

their accelerations is correct?

A) The acceleration of A is greater than the acceleration of B.

B) The acceleration of B is greater than the acceleration of A.

C) The two bricks have exactly the same acceleration.

D) Neither brick has any acceleration once it is released.

C) a straight line making an angle with the time axis.
An object is moving with constant non-zero velocity in the +x direction. The position versus time graph of this object is

A) a horizontal straight line.

B) a vertical straight line.

C) a straight line making an angle with the time axis.

D) a parabolic curve.

B) velocity.
The slope of a position versus time graph gives

A) the distance traveled.

B) velocity.

C) acceleration.

D) displacement.

C) at rest.
If the position versus time graph of an object is a horizontal line, the object is

A) moving with constant non-zero speed.

B) moving with constant non-zero acceleration.

C) at rest.

D) moving with increasing speed.

B) moving with constant non-zero acceleration.
42) If the velocity versus time graph of an object is a straight line making an angle of +30° (counter clockwise) with the time axis, the object is

A) moving with constant non-zero speed.

B) moving with constant non-zero acceleration.

C) at rest.

D) moving with increasing acceleration.

D) The truck will have travelled further than the car.
43) The motions of a car and a truck along a straight road are represented by the velocity-time graphs in the figure. The two vehicles are initially alongside each other at time t = 0. At time T, what is true of the distances traveled by the vehicles since time t = 0?

A) They will have traveled the same distance.

B) The truck will not have moved.

C) The car will have travelled further than the truck.

D) The truck will have travelled further than the car.

A) graph a
Which of the following graphs represent an object at rest? (There could be more than one correct choice.)

A) graph a

B) graph b

C) graph c

D) graph d

E) graph e

C) graphs a and b
45) Which of the following graphs represent an object having zero acceleration?

A) only graph a

B) only graph b

C) graphs a and b

D) graphs b and c

E) graphs c and d

D) Both cars have the same acceleration.

E) The cars meet at time t = 10 s.

The figure shows a graph of the position x of two cars, C and D, as a function of time t.

According to this graph, which statements about these cars must be true? (There could be more than one correct choice.)

A) The magnitude of the acceleration of car C is greater than the magnitude of the acceleration of car D.

B) The magnitude of the acceleration of car C is less than the magnitude of the acceleration of car D.

C) At time t = 10 s, both cars have the same velocity.

D) Both cars have the same acceleration.

E) The cars meet at time t = 10 s.

D) decreases and then increases.
The motion of a particle is described in the velocity vs. time graph shown in the figure. Over the nine-second interval shown, we can say that the speed of the particle

A) only increases.

B) only decreases.

C) increases and then decreases.

D) decreases and then increases.

E) remains constant.

D) 3 s
he graph in the figure shows the position of a particle as it travels along the x-axis. At what value of t is the speed of the particle equal to 0 m/s?

A) 0 s

B) 1 s

C) 2 s

D) 3 s

E) 4 s

C) displacement.
The area under a curve in a velocity versus time graph gives

A) acceleration.

B) velocity.

C) displacement.

D) position.

False
If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude.
(t or f)
D) could be as small as 2.0 m or as large as 12 m.
Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors

are added together, the magnitude of the sum

A) is equal to 2.0 m.

B) is equal to 12 m.

C) is equal to 8.6 m.

D) could be as small as 2.0 m or as large as 12 m.

40mm
Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant?

A) 40 mm B) 80 mm C) 20 mm D) 10 mm

False
The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.
(t or f)
false
If A – B = 0, then the vectors A and B have equal magnitudes and are directed in the same direction.
(t or f)
false
If three vectors add to zero, they must all have equal magnitudes.
The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is

A) 60° B) 270° C) 0° D) 90° E) 180°

180
The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is

A) 180° B) 0° C) 360° D) 270° E) 90°

C) Vectors M and N have the same magnitudes.
Vectors M and N obey the equation M + N = 0. These vectors satisfy which one of the

following statements?

A) Vectors M and N are at right angles to each other.

B) The magnitude of M is the negative of the magnitude of N .

C) Vectors M and N have the same magnitudes.

D) Vectors M and N point in the same direction.

false
If a vector’s components are all negative, then the magnitude of the vector is negative.
true
The magnitude of a vector an only zero ifall of its components are zero.
A) 90° to 180°
If a vector A has componentsAx< 0, andAy > 0, then the angle that this vector makes with the positivex-axis must be in the range

A) 90° to 180°

B) 0° to 90°

C) 270° to 360°

D) 180° to 270°

E) It cannot be determined without additional information.

A) 180° to 270°
If a vector A has componentsAx< 0, andAy < 0, then the angle that this vector makes with the positivex-axis must be in the range A) 180° to 270° B) 0° to 90° C) 270° to 360° D) 90° to 180° E) cannot be determined without additional information
B) The magnitude of vector A must be equal to the magnitude of vector B .
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 must be correct for

these two vectors?

A) Vector A is parallel to vector B .

B) The magnitude of vector A must be equal to the magnitude of vector B .

C) Vector A is antiparallel (in the opposite direction) to vector B .

D) The angle between vector A and vector B must be 90°.

E) Vector A must be perpendicular to vector B .

A) remains a non-zero constant.
For general projectile motion with no air resistance, the horizontal component of a projectile’s

velocity

A) remains a non-zero constant.

B) continuously decreases.

C) first decreases and then increases.

D) continuously increases.

E) remains zero.

E) is always zero.
For general projectile motion with no air resistance, the horizontal component of a projectile’s

acceleration

A) continuously increases.

B) first decreases and then increases.

C) remains a non-zero constant.

D) continuously decreases.

E) is always zero.

C) remains a non-zero constant.
For general projectile motion with no air resistance, the vertical component of a projectile’s

acceleration

A) first decreases and then increases.

B) continuously decreases.

C) remains a non-zero constant.

D) continuously increases.

E) is always zero.

A) The horizontal acceleration is always zero and the vertical acceleration is always a

non-zero constant downward.

Which of the following statements are true about an object in two-dimensional projectile motion

with no air resistance? (There could be more than one correct choice.)

A) The horizontal acceleration is always zero and the vertical acceleration is always a

non-zero constant downward.

B) The speed of the object is constant but its velocity is not constant.

C) The speed of the object is zero at its highest point.

D) The acceleration of the object is +g when the object is rising and -g when it is falling.

E) The acceleration of the object is zero at its highest point.

The ball
A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped

vertically. Which object is traveling faster when it hits the level ground below if neither of them

experiences any air resistance?

A) It is impossible to tell because we do not know their masses.

B) the ball

C) the stone

D) Both are traveling at the same speed.

They hit at the same time
In an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble

is dropped from the same height. Compare the times of fall of the two pebbles.

A) They hit at the same time.

B) The dropped pebble hits first.

C) The thrown pebble hits first.

D) We cannot tell without knowing which pebble is heavier.

D) be directly over the package.
A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

A) be in front of the package.

B) depend on the speed of the plane when the package was released.

C) be behind the package.

D) be directly over the package.

C) the splashdown speed of John is larger than that of James.
James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. If there is no air resistance, when they reach the lake below

A) they will both have the same splashdown speed.

B) the splashdown speed of James must be 9.8 m/s larger than that of John.

C) the splashdown speed of John is larger than that of James.

D) the splashdown speed of James is larger than that of John.

E) the splashdown speed of John must be 25 m/s larger than that of James.

C) James and John will reach the surface of the lake at the same time.
James and John dive from an overhang into the lake below. James simply drops straight down

from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s.

Compare the time it takes each to reach the lake below if there is no air resistance.

A) John reaches the surface of the lake first.

B) Cannot be determined without knowing the mass of both James and John.

C) James and John will reach the surface of the lake at the same time.

D) Cannot be determined without knowing the weight of both James and John.

E) James reaches the surface of the lake first.

E) neither the ball’s velocity nor its acceleration are zero.
A player kicks a soccer ball in a high arc toward the opponent’s goal. At the highest point in its

trajectory

A) the ball’s velocity points downward.

B) the ball’s acceleration is zero but its velocity is not zero.

C) both the velocity and the acceleration of the soccer ball are zero.

D) the ball’s acceleration points upward.

E) neither the ball’s velocity nor its acceleration are zero.

B) Both snowballs will hit the ground with the same speed.
Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the following statements are true about just as the snowballs reach the ground below? (There could be more than one correct choice.)

A) Debra’s snowball will have a higher speed than Mary’s snowball.

B) Both snowballs will hit the ground with the same speed.

C) Mary’s snowball will have a higher speed than Debra’s snowball.

D) Mary’s snowball reaches the ground before Debra’s snowball.

E) Both snowballs hit the ground at the same time.

E) Debra’s snowball will stay in the air longer than Mary’s snowball.
33) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial

speed, but in different directions. Mary throws her snowball downward, at 30° below the

horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the

following statements are true about just before the snowballs reach the ground below? (There

could be more than one correct choice.)

A) Mary’s snowball will stay in the air longer than Debra’s snowball.

B) Mary’s snowball has a greater downward acceleration than Debra’s snowball.

C) Both snowballs will take the same amount of time to hit the ground.

D) Debra’s snowball has exactly the same acceleration as Mary’s snowball.

E) Debra’s snowball will stay in the air longer than Mary’s snowball.

E) Its horizontal velocity component is the same as it was just as it was launched.
A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which of the following statements about the rock’s motion are true just before it hits the ground? (There could be more than one correct choice.)

A) Its vertical velocity component is the same as it was just as it was launched.

B) Its velocity is vertical.

C) Its horizontal velocity component is zero.

D) Its speed is the same as it was just as it was launched.

E) Its horizontal velocity component is the same as it was just as it was launched.

D) The vectors are perpendicular to each other.
An object moves in a circular path at a constant speed. Compare the direction of the object’s velocity and acceleration vectors.

A) Both vectors point in the same direction.

B) The acceleration is zero but the velocity is constant.

C) The vectors point in opposite directions.

D) The vectors are perpendicular to each other.

false
37) The Moon is accelerated toward the earth, so it is gradually getting closer to the earth.

A) True

B) False

C) The moon is not accelerated toward the earth.

B) in a general northwesterly direction.
You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

A) in a general southwesterly direction.
B) in a general northwesterly direction.
C) directly toward the west.
D) directly toward the north.

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